Calculus of a Single Variable
Calculus of a Single Variable
11th Edition
ISBN: 9781337275361
Author: Ron Larson, Bruce H. Edwards
Publisher: Cengage Learning
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Concept explainers

Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
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Chapter 4.3, Problem 51E

Think About It A function f is defined below. Use geometric formulas to find ∫ 0 8 f ( x ) d x .

f ( x ) = { 4 ,       x < 4 x ,     x ≥ 4

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Chapter 4 Solutions

Calculus of a Single Variable

Ch. 4.1 - CONCEPT CHECK Antiderivative What does it mean for...Ch. 4.1 - Prob. 2ECh. 4.1 - Prob. 3ECh. 4.1 - General and Particular Solutions Describe the...Ch. 4.1 - Integration and Differentiation In Exercises 5 and...Ch. 4.1 - Prob. 6ECh. 4.1 - Solving a Differential Equation In Exercises 7-10,...Ch. 4.1 - Solving a Differential Equation In Exercises 7-10,...Ch. 4.1 - Solving a Differential Equation In Exercises 7-10,...Ch. 4.1 - Solving a Differential Equation In Exercises 7-10,...
Ch. 4.1 - Rewriting Before Integrating In Exercises 11-14,...Ch. 4.1 - Rewriting Before Integrating In Exercises 11-14,...Ch. 4.1 - Rewriting Before Integrating In Exercises 11-14,...Ch. 4.1 - Rewriting Before Integrating In Exercises 11-14,...Ch. 4.1 - Finding an Indefinite Integral In Exercises 15-36,...Ch. 4.1 - Finding an Indefinite Integral In Exercises 15-36,...Ch. 4.1 - Finding an Indefinite Integral In Exercises 15-36,...Ch. 4.1 - Finding an Indefinite Integral In Exercises 15-36,...Ch. 4.1 - Prob. 20ECh. 4.1 - Prob. 18ECh. 4.1 - Finding an Indefinite Integral In Exercises 15-36,...Ch. 4.1 - Prob. 28ECh. 4.1 - Prob. 23ECh. 4.1 - Prob. 24ECh. 4.1 - Finding an Indefinite Integral In Exercises 15-36,...Ch. 4.1 - Prob. 26ECh. 4.1 - Finding an Indefinite Integral In Exercises 15-36,...Ch. 4.1 - Prob. 30ECh. 4.1 - Prob. 21ECh. 4.1 - Prob. 22ECh. 4.1 - Finding an Indefinite Integral In Exercises 15-36,...Ch. 4.1 - Prob. 34ECh. 4.1 - Finding an Indefinite Integral In Exercises 15-36,...Ch. 4.1 - Prob. 36ECh. 4.1 - Prob. 31ECh. 4.1 - Prob. 32ECh. 4.1 - Prob. 37ECh. 4.1 - Prob. 38ECh. 4.1 - Finding a Particular Solution In Exercises 37-44,...Ch. 4.1 - Prob. 40ECh. 4.1 - Finding a Particular Solution In Exercises 37-44,...Ch. 4.1 - Prob. 42ECh. 4.1 - Prob. 43ECh. 4.1 - Prob. 44ECh. 4.1 - Prob. 45ECh. 4.1 - Slope Field In Exercises 45 and 46, a differential...Ch. 4.1 - Prob. 47ECh. 4.1 - Prob. 48ECh. 4.1 - Prob. 49ECh. 4.1 - Prob. 50ECh. 4.1 - Comparing Functions Consider f(x)=tan2x and...Ch. 4.1 - HOW DO YOU SEE IT? Use the graph of f shown in the...Ch. 4.1 - Prob. 53ECh. 4.1 - Sketching Graphs The graphs of f and f each pass...Ch. 4.1 - Tree Growth An evergreen nursery usually sells a...Ch. 4.1 - Population Growth The rate of growth dP/dt of a...Ch. 4.1 - Vertical Motion In Exercises 57-59, assume the...Ch. 4.1 - Vertical Motion In Exercises 57-59, assume the...Ch. 4.1 - Vertical Motion In Exercises 57-59, assume the...Ch. 4.1 - Vertical Motion In Exercises 60-62, assume the...Ch. 4.1 - Vertical Motion In Exercises 60-62, assume the...Ch. 4.1 - Prob. 62ECh. 4.1 - Lunar Gravity On the moon, the acceleration of a...Ch. 4.1 - Escape Velocity The minimum velocity required for...Ch. 4.1 - Prob. 65ECh. 4.1 - Prob. 66ECh. 4.1 - Rectilinear Motion In Exercises 65-68, consider a...Ch. 4.1 - Rectilinear Motion In Exercises 65-68, consider a...Ch. 4.1 - Acceleration The maker of an automobile advertises...Ch. 4.1 - Deceleration A car traveling at 45 miles per hour...Ch. 4.1 - Prob. 71ECh. 4.1 - Acceleration Assume that a fully loaded plane...Ch. 4.1 - Prob. 73ECh. 4.1 - Prob. 74ECh. 4.1 - Prob. 79ECh. 4.1 - Prob. 80ECh. 4.1 - Prob. 75ECh. 4.1 - True or False? In Exercises 73-78, determine...Ch. 4.1 - Prob. 77ECh. 4.1 - Prob. 81ECh. 4.1 - Prob. 78ECh. 4.2 - Prob. 1ECh. 4.2 - CONCEPT CHECK Sums What is the value of n? (a)...Ch. 4.2 - Prob. 3ECh. 4.2 - Prob. 4ECh. 4.2 - Finding a Sum In Exercises 5-10, find the sum by...Ch. 4.2 - Prob. 6ECh. 4.2 - Finding a Sum In Exercises 5-10, find the sum by...Ch. 4.2 - Prob. 8ECh. 4.2 - Finding a Sum In Exercises 5-10, find the sum by...Ch. 4.2 - Finding a Sum In Exercises 5-10, find the sum by...Ch. 4.2 - Using Sigma Notation In Exercises 11-16, use sigma...Ch. 4.2 - Prob. 12ECh. 4.2 - Prob. 13ECh. 4.2 - Prob. 14ECh. 4.2 - Using Sigma Notation In Exercises 11-16, use sigma...Ch. 4.2 - Prob. 16ECh. 4.2 - Evaluating a Sum In Exercises 17-24, use the...Ch. 4.2 - Evaluating a Sum In Exercises 17-24, use the...Ch. 4.2 - Evaluating a Sum In Exercises 17-24, use the...Ch. 4.2 - Evaluating a Sum In Exercises 17-24, use the...Ch. 4.2 - Evaluating a Sum In Exercises 17-24, use the...Ch. 4.2 - Prob. 22ECh. 4.2 - Evaluating a Sum In Exercises 1724, use the...Ch. 4.2 - Prob. 24ECh. 4.2 - Prob. 25ECh. 4.2 - Evaluating a Sum In Exercises 2528, use the...Ch. 4.2 - Evaluating a Sum In Exercises 25-28, use the...Ch. 4.2 - Prob. 28ECh. 4.2 - Approximating the Area of a Plane Region In...Ch. 4.2 - Prob. 30ECh. 4.2 - Approximating the Area of a Plane Region In...Ch. 4.2 - Prob. 32ECh. 4.2 - Prob. 33ECh. 4.2 - Prob. 34ECh. 4.2 - Prob. 35ECh. 4.2 - Using Upper and Lower Sums In Exercises 35 and 36,...Ch. 4.2 - Prob. 37ECh. 4.2 - Prob. 38ECh. 4.2 - Finding Upper and Lower Sums for a Region In...Ch. 4.2 - Prob. 40ECh. 4.2 - Finding Upper and Lower Sums for a Region In...Ch. 4.2 - Finding Upper and Lower Sums for a Region In...Ch. 4.2 - Finding Upper and Lower Sums for a Region In...Ch. 4.2 - Finding Upper and Lower Sums for a Region In...Ch. 4.2 - Prob. 45ECh. 4.2 - Prob. 46ECh. 4.2 - Prob. 47ECh. 4.2 - Prob. 48ECh. 4.2 - Prob. 49ECh. 4.2 - Prob. 50ECh. 4.2 - Prob. 51ECh. 4.2 - Prob. 52ECh. 4.2 - Prob. 53ECh. 4.2 - Prob. 54ECh. 4.2 - Prob. 55ECh. 4.2 - Prob. 56ECh. 4.2 - Prob. 57ECh. 4.2 - Prob. 58ECh. 4.2 - Prob. 59ECh. 4.2 - Prob. 60ECh. 4.2 - Prob. 61ECh. 4.2 - Prob. 62ECh. 4.2 - Prob. 63ECh. 4.2 - Prob. 64ECh. 4.2 - Prob. 65ECh. 4.2 - Prob. 66ECh. 4.2 - Prob. 67ECh. 4.2 - Prob. 68ECh. 4.2 - Prob. 69ECh. 4.2 - EXPLORING CONCEPTS Midpoint Rule Does the Midpoint...Ch. 4.2 - Graphical Reasoning Consider the region bounded by...Ch. 4.2 - Prob. 72ECh. 4.2 - Prob. 73ECh. 4.2 - Prob. 74ECh. 4.2 - Prob. 75ECh. 4.2 - Prob. 76ECh. 4.2 - Seating Capacity A teacher places n scats to form...Ch. 4.2 - Prob. 78ECh. 4.2 - Prob. 79ECh. 4.3 - CONCEPT CHECK Riemann Sum What does a Riemann Mini...Ch. 4.3 - Prob. 2ECh. 4.3 - Prob. 3ECh. 4.3 - Prob. 4ECh. 4.3 - Evaluating a Definite Integral as a Limit In...Ch. 4.3 - Prob. 6ECh. 4.3 - Prob. 7ECh. 4.3 - Prob. 8ECh. 4.3 - Evaluating a Definite Integral as a Limit In...Ch. 4.3 - Prob. 10ECh. 4.3 - Prob. 11ECh. 4.3 - Prob. 12ECh. 4.3 - Prob. 13ECh. 4.3 - Prob. 14ECh. 4.3 - Writing a Definite Integral In Exercises 13-22,...Ch. 4.3 - Prob. 16ECh. 4.3 - Prob. 17ECh. 4.3 - Prob. 18ECh. 4.3 - Prob. 19ECh. 4.3 - Prob. 20ECh. 4.3 - Writing a Definite Integral In Exercises 13-22,...Ch. 4.3 - Prob. 22ECh. 4.3 - Prob. 23ECh. 4.3 - Prob. 24ECh. 4.3 - Prob. 25ECh. 4.3 - Prob. 26ECh. 4.3 - Prob. 27ECh. 4.3 - Prob. 28ECh. 4.3 - Evaluating a Definite Integral Using a Geometric...Ch. 4.3 - Evaluating a Definite Integral Using a Geometric...Ch. 4.3 - Evaluating a Definite Integral Using a Geometric...Ch. 4.3 - Prob. 32ECh. 4.3 - Prob. 33ECh. 4.3 - Prob. 34ECh. 4.3 - Prob. 35ECh. 4.3 - Prob. 36ECh. 4.3 - Prob. 37ECh. 4.3 - Using Properties of Definite Integrals In...Ch. 4.3 - Prob. 39ECh. 4.3 - Prob. 40ECh. 4.3 - Using Properties of Definite Integrals Given...Ch. 4.3 - Prob. 42ECh. 4.3 - Prob. 43ECh. 4.3 - Prob. 44ECh. 4.3 - Estimating a Definite Integral Use the table of...Ch. 4.3 - Estimating a Definite Integral Use the table of...Ch. 4.3 - Think About It The graph of f consists of line...Ch. 4.3 - Think About It The graph of f consists of line...Ch. 4.3 - Prob. 49ECh. 4.3 - Prob. 50ECh. 4.3 - Think About It A function f is defined below. Use...Ch. 4.3 - Prob. 52ECh. 4.3 - Prob. 53ECh. 4.3 - Prob. 54ECh. 4.3 - Prob. 55ECh. 4.3 - Prob. 56ECh. 4.3 - Prob. 57ECh. 4.3 - Prob. 58ECh. 4.3 - Prob. 59ECh. 4.3 - Prob. 60ECh. 4.3 - Prob. 61ECh. 4.3 - Prob. 62ECh. 4.3 - Prob. 63ECh. 4.3 - Prob. 64ECh. 4.3 - Prob. 65ECh. 4.3 - Prob. 66ECh. 4.3 - Prob. 67ECh. 4.3 - Prob. 68ECh. 4.3 - Prob. 69ECh. 4.3 - Finding a Riemann Sum Find the Riemann sum for...Ch. 4.3 - Prob. 71ECh. 4.3 - Prob. 72ECh. 4.3 - Prob. 73ECh. 4.3 - Prob. 74ECh. 4.3 - Finding Values Find the constants a and b that...Ch. 4.3 - Prob. 76ECh. 4.3 - Prob. 77ECh. 4.3 - Prob. 78ECh. 4.3 - Prob. 79ECh. 4.4 - CONCEPT CHECK Fundamental Theorem of Calculus...Ch. 4.4 - Prob. 2ECh. 4.4 - Prob. 3ECh. 4.4 - Prob. 4ECh. 4.4 - Graphical Reasoning In Exercises 58, use a...Ch. 4.4 - Graphical Reasoning In Exercises 58, use a...Ch. 4.4 - Prob. 7ECh. 4.4 - Prob. 8ECh. 4.4 - Evaluating a Definite Integral In Exercises 936,...Ch. 4.4 - Evaluating a Definite Integral In Exercises 936,...Ch. 4.4 - Evaluating a Definite Integral In Exercises 9-36,...Ch. 4.4 - Evaluating a Definite Integral In Exercises 9-36,...Ch. 4.4 - Evaluating a Definite Integral In Exercises 936,...Ch. 4.4 - Evaluating a Definite Integral In Exercises 936,...Ch. 4.4 - Evaluating a Definite Integral In Exercises 936,...Ch. 4.4 - Evaluating a Definite Integral In Exercises 936,...Ch. 4.4 - Evaluating a Definite Integral In Exercises 936,...Ch. 4.4 - Evaluating a Definite Integral In Exercises 936,...Ch. 4.4 - Evaluating a Definite Integral In Exercises 936,...Ch. 4.4 - Evaluating a Definite Integral In Exercises 936,...Ch. 4.4 - Evaluating a Definite Integral In Exercises 9-36,...Ch. 4.4 - Evaluating a Definite Integral In Exercises 9-36,...Ch. 4.4 - Evaluating a Definite Integral In Exercises 9-36,...Ch. 4.4 - Prob. 24ECh. 4.4 - Prob. 25ECh. 4.4 - Prob. 26ECh. 4.4 - Prob. 27ECh. 4.4 - Prob. 28ECh. 4.4 - Prob. 29ECh. 4.4 - Prob. 30ECh. 4.4 - Prob. 31ECh. 4.4 - Prob. 32ECh. 4.4 - Prob. 33ECh. 4.4 - Prob. 34ECh. 4.4 - Prob. 35ECh. 4.4 - Prob. 36ECh. 4.4 - Prob. 37ECh. 4.4 - Prob. 38ECh. 4.4 - Prob. 39ECh. 4.4 - Prob. 40ECh. 4.4 - Prob. 41ECh. 4.4 - Prob. 42ECh. 4.4 - Prob. 43ECh. 4.4 - Prob. 45ECh. 4.4 - Finding the Area of a Region In Exercises 41-46,...Ch. 4.4 - Prob. 46ECh. 4.4 - Prob. 47ECh. 4.4 - Prob. 48ECh. 4.4 - Prob. 49ECh. 4.4 - Prob. 50ECh. 4.4 - Prob. 51ECh. 4.4 - Using the Mean Value Theorem for Integrals In...Ch. 4.4 - Prob. 53ECh. 4.4 - Prob. 54ECh. 4.4 - Prob. 55ECh. 4.4 - Prob. 56ECh. 4.4 - Finding the Average Value of a Function In...Ch. 4.4 - Prob. 58ECh. 4.4 - Force The force F (in newtons) of a hydraulic...Ch. 4.4 - Respiratory Cycle The volume V in liters, of air...Ch. 4.4 - Prob. 61ECh. 4.4 - HOW DO YOU SEE IT? The graph of f is shown in the...Ch. 4.4 - Prob. 63ECh. 4.4 - Prob. 64ECh. 4.4 - Prob. 65ECh. 4.4 - Prob. 66ECh. 4.4 - Analyzing a Function Let g(x)=0xf(t)dt where f is...Ch. 4.4 - Analyzing a Function Let g(x)=0xf(t)dt where f is...Ch. 4.4 - Prob. 69ECh. 4.4 - Prob. 70ECh. 4.4 - Prob. 71ECh. 4.4 - Prob. 72ECh. 4.4 - Finding and Checking an Integral In Exercises...Ch. 4.4 - Prob. 74ECh. 4.4 - Prob. 75ECh. 4.4 - Prob. 76ECh. 4.4 - Prob. 77ECh. 4.4 - Prob. 78ECh. 4.4 - Prob. 79ECh. 4.4 - Prob. 80ECh. 4.4 - Finding a Derivative In Exercises 81-86, find F( x...Ch. 4.4 - Finding a Derivative In Exercises 81-86, find F( x...Ch. 4.4 - Prob. 83ECh. 4.4 - Prob. 84ECh. 4.4 - Prob. 85ECh. 4.4 - Prob. 86ECh. 4.4 - Graphical Analysis Sketch an approximate graph of...Ch. 4.4 - Prob. 88ECh. 4.4 - Water Flow Water flows from a storage tank at a...Ch. 4.4 - Oil Leak At 1:00 p.m., oil begins leaking from a...Ch. 4.4 - Velocity The graph shows the velocity, in feet per...Ch. 4.4 - Prob. 92ECh. 4.4 - Particle Motion In Exercises 93-98, the velocity...Ch. 4.4 - Prob. 94ECh. 4.4 - Prob. 95ECh. 4.4 - Prob. 96ECh. 4.4 - Prob. 97ECh. 4.4 - Prob. 98ECh. 4.4 - Prob. 99ECh. 4.4 - Prob. 100ECh. 4.4 - Prob. 101ECh. 4.4 - Prob. 102ECh. 4.4 - Prob. 103ECh. 4.4 - Prob. 104ECh. 4.4 - Prob. 105ECh. 4.4 - Prob. 106ECh. 4.4 - Prob. 107ECh. 4.4 - Prob. 108ECh. 4.4 - Prob. 109ECh. 4.4 - Prob. 110ECh. 4.4 - Prob. 111ECh. 4.4 - Finding a Function Find the function f(x) and all...Ch. 4.4 - Prob. 113ECh. 4.4 - Prob. 114ECh. 4.4 - PUTNAM EXAM CHALLENGE For each continuous function...Ch. 4.5 - CONCEPT CHECK Constant Multiple Rule Explain how...Ch. 4.5 - Prob. 2ECh. 4.5 - CONCEPT CHECK The General Power Rule for...Ch. 4.5 - Prob. 4ECh. 4.5 - Recognizing Patterns In Exercises 5-8, complete...Ch. 4.5 - Recognizing Patterns In Exercises 5-8, complete...Ch. 4.5 - Recognizing Patterns In Exercises 5-8, complete...Ch. 4.5 - Prob. 8ECh. 4.5 - Finding an Indefinite Integral In Exercises 9-30,...Ch. 4.5 - Prob. 10ECh. 4.5 - Finding an Indefinite Integral In Exercises 9-30,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 9-30,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 9-30,...Ch. 4.5 - Prob. 14ECh. 4.5 - Prob. 15ECh. 4.5 - Prob. 16ECh. 4.5 - Prob. 17ECh. 4.5 - Finding an Indefinite Integral In Exercises 9-30,...Ch. 4.5 - Prob. 18ECh. 4.5 - Prob. 20ECh. 4.5 - Finding an Indefinite Integral In Exercises 9-30,...Ch. 4.5 - Prob. 22ECh. 4.5 - Prob. 23ECh. 4.5 - Prob. 24ECh. 4.5 - Finding an Indefinite Integral In Exercises 9-30,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 9-30,...Ch. 4.5 - Prob. 27ECh. 4.5 - Prob. 28ECh. 4.5 - Finding an Indefinite Integral In Exercises 9-30,...Ch. 4.5 - Prob. 30ECh. 4.5 - Differential Equation In Exercises 31-34, find the...Ch. 4.5 - Prob. 32ECh. 4.5 - Differential Equation In Exercises 31-34, find the...Ch. 4.5 - Differential Equation In Exercises 31-34, find the...Ch. 4.5 - Prob. 35ECh. 4.5 - Prob. 36ECh. 4.5 - Prob. 37ECh. 4.5 - Prob. 38ECh. 4.5 - Prob. 39ECh. 4.5 - Prob. 40ECh. 4.5 - Finding an Indefinite Integral In Exercises 39-48,...Ch. 4.5 - Finding an Indefinite Integral In Exercises 39-48,...Ch. 4.5 - Prob. 43ECh. 4.5 - Prob. 44ECh. 4.5 - Prob. 45ECh. 4.5 - Prob. 46ECh. 4.5 - Prob. 47ECh. 4.5 - Prob. 48ECh. 4.5 - Prob. 51ECh. 4.5 - Prob. 52ECh. 4.5 - Prob. 49ECh. 4.5 - Finding an Equation Exercises 49-52, find an...Ch. 4.5 - Change of Variables In Exercises 53-60, find the...Ch. 4.5 - Prob. 54ECh. 4.5 - Change of Variables In Exercises 53-60, find the...Ch. 4.5 - Prob. 56ECh. 4.5 - Change of Variables In Exercises 53-60, find the...Ch. 4.5 - Prob. 58ECh. 4.5 - Prob. 59ECh. 4.5 - Prob. 60ECh. 4.5 - Prob. 71ECh. 4.5 - Prob. 72ECh. 4.5 - Prob. 61ECh. 4.5 - Prob. 62ECh. 4.5 - Prob. 63ECh. 4.5 - Evaluating a Definite Integral In Exercises 61-68,...Ch. 4.5 - Prob. 65ECh. 4.5 - Prob. 66ECh. 4.5 - Prob. 67ECh. 4.5 - Prob. 68ECh. 4.5 - Prob. 69ECh. 4.5 - Prob. 70ECh. 4.5 - Prob. 73ECh. 4.5 - Prob. 74ECh. 4.5 - Prob. 75ECh. 4.5 - Prob. 76ECh. 4.5 - Prob. 77ECh. 4.5 - Using Symmetry Use the symmetry of the graphs of...Ch. 4.5 - Prob. 79ECh. 4.5 - Prob. 80ECh. 4.5 - Prob. 81ECh. 4.5 - Prob. 82ECh. 4.5 - Depreciation The rate of depreciation dV/dt of a...Ch. 4.5 - HOW DO YOU SEE IT? The graph shows the flow rate...Ch. 4.5 - Prob. 85ECh. 4.5 - Electricity The oscillating current in an...Ch. 4.5 - Prob. 87ECh. 4.5 - Prob. 88ECh. 4.5 - Prob. 89ECh. 4.5 - Prob. 90ECh. 4.5 - Prob. 91ECh. 4.5 - Prob. 92ECh. 4.5 - True or False? In Exercises 9398, determine...Ch. 4.5 - Prob. 94ECh. 4.5 - Prob. 95ECh. 4.5 - Prob. 96ECh. 4.5 - Prob. 97ECh. 4.5 - True or False? In Exercises 9398, determine...Ch. 4.5 - Prob. 99ECh. 4.5 - Prob. 100ECh. 4.5 - Prob. 101ECh. 4.5 - Prob. 102ECh. 4.5 - Prob. 103ECh. 4.5 - Prob. 104ECh. 4 - Finding an Indefinite Integral In Exercises 1-8,...Ch. 4 - Prob. 2RECh. 4 - Prob. 3RECh. 4 - Prob. 4RECh. 4 - Prob. 5RECh. 4 - Prob. 8RECh. 4 - Prob. 6RECh. 4 - Prob. 7RECh. 4 - Prob. 9RECh. 4 - Prob. 10RECh. 4 - Finding a Particular Solution In Exercises 9-12,...Ch. 4 - Prob. 12RECh. 4 - Prob. 13RECh. 4 - Vertical Motion With what initial velocity must an...Ch. 4 - Prob. 15RECh. 4 - Prob. 16RECh. 4 - Prob. 17RECh. 4 - Prob. 18RECh. 4 - Prob. 21RECh. 4 - Prob. 22RECh. 4 - Prob. 23RECh. 4 - Evaluating a Sum In Exercises 1924, use the...Ch. 4 - Prob. 19RECh. 4 - Prob. 20RECh. 4 - Prob. 27RECh. 4 - Prob. 28RECh. 4 - Prob. 29RECh. 4 - Prob. 30RECh. 4 - Prob. 31RECh. 4 - Prob. 32RECh. 4 - Prob. 25RECh. 4 - Prob. 26RECh. 4 - Prob. 33RECh. 4 - Prob. 34RECh. 4 - Prob. 35RECh. 4 - Prob. 36RECh. 4 - Prob. 37RECh. 4 - Prob. 38RECh. 4 - Prob. 39RECh. 4 - Prob. 40RECh. 4 - Prob. 43RECh. 4 - Prob. 46RECh. 4 - Prob. 41RECh. 4 - Prob. 42RECh. 4 - Prob. 49RECh. 4 - Prob. 52RECh. 4 - Prob. 44RECh. 4 - Prob. 45RECh. 4 - Prob. 53RECh. 4 - Using the Mean Value Theorem for Integrals In...Ch. 4 - Finding the Average Value of a Function In...Ch. 4 - Prob. 56RECh. 4 - Finding the Area of a Region In Exercises 47 and...Ch. 4 - Prob. 48RECh. 4 - Prob. 57RECh. 4 - Prob. 58RECh. 4 - Prob. 50RECh. 4 - Prob. 51RECh. 4 - Prob. 60RECh. 4 - Prob. 59RECh. 4 - Prob. 63RECh. 4 - Prob. 61RECh. 4 - Prob. 62RECh. 4 - Prob. 64RECh. 4 - Prob. 65RECh. 4 - Prob. 66RECh. 4 - Prob. 67RECh. 4 - Prob. 68RECh. 4 - Prob. 69RECh. 4 - Prob. 70RECh. 4 - Evaluating a Definite Integral In Exercises 67-72,...Ch. 4 - Prob. 72RECh. 4 - Finding the Area of a Region In Exercises 73 and...Ch. 4 - Prob. 74RECh. 4 - Prob. 75RECh. 4 - Prob. 76RECh. 4 - Prob. 1PSCh. 4 - Parabolic Arch Archimedes showed that the area of...Ch. 4 - Prob. 14PSCh. 4 - Prob. 5PSCh. 4 - Prob. 6PSCh. 4 - Prob. 7PSCh. 4 - Prob. 8PSCh. 4 - Prob. 9PSCh. 4 - Prob. 10PSCh. 4 - Prob. 11PSCh. 4 - Prob. 12PSCh. 4 - Prob. 13PSCh. 4 - Velocity and Acceleration A car travels in a...Ch. 4 - Prob. 16PSCh. 4 - Prob. 17PSCh. 4 - Prob. 3PSCh. 4 - Prob. 4PSCh. 4 - Prob. 18PSCh. 4 - Upper and Lower Sums Consider the region bounded...Ch. 4 - Prob. 20PSCh. 4 - Finding a Function The graph of f' is shown. Find...
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Differential Equation | MIT 18.01SC Single Variable Calculus, Fall 2010; Author: MIT OpenCourseWare;https://www.youtube.com/watch?v=HaOHUfymsuk;License: Standard YouTube License, CC-BY