Use Simpson's Rule and all the data in the following table to estimate the value of the integral X -11 -10 -9 -8 -7 -6 -5 y -3 6 -5 4 6 -5 1 Round your answer to 4 decimal places -5 ydx. -11

Approximate L 5 1 dx using the midpoint rule with five subdivisions to four decimal places. In(x) The approximation is:

Evaluate the integral: 3 · Sz³ √4 – x²dz + C

Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If it diverges to infinity, state your answer as "oo" (without the quotation marks). If it diverges to negative infinity, state your answer as "-00". If it diverges without being infinity or negative infinity, state your answer as "DNE". .8 1 dx 0 x0.3

Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not, state your answer as "DNE" 1 1 dx -∞ x²+1

The partial fraction decomposition of f(x) x +4 g(x) + where ' x² +4 f(x) = g(x) = 8x218x44 can be written in the form of x34x2+4x+16

Use the substitution = 7 tan(0) to evaluate the indefinite integral 99dx + C

4 The partial fraction decomposition of can be written in the form of x² - 25 f(x) = g(x) = f(x) g(x) where + x - 5 x+5

Select the best technique to integrate each function. リ xedx .2 x+9 2 +5 +6 3 -dx √2² (2 – 2³)³dr - √ √ x² (3x + 9)dx リ x3 4-x2 - dx a. Algebraic manipulation or direct integration b. Substitution c. Integration by parts d. Trig substitution e. Partial fractions