Given information: Given curves y=1−x2,y=0

Calculation:

Draw the graph of y=1−x2,y=0 rotate around x−axis .

Area of typical disk:

  A=πr2 A=π(1−x2)2             Since  r=1−x2

Volume =∫abA(x)dx, where A(x)= area of typical disk.

Here X values for this graph range from 0 to 1 thus, a=0 , b=1 .

  A(x)=π∫01(1−x2)2

  A(x)=π∫01(1−2x2+x4)dx

Integrate each term using power rule, ∫abxndx=xn+1n+1+c

  A(x)=π[x−23x3+15x5]01

Use fundamental theorem, ∫abf(x)dx=F(b)−F(a)  where F(X) is the Ant derivative of f(x)

  =π{[1−23(1)3+15(1)5]−(0)}

  =8π15

Thus, volume of the solid obtained by rotating the region bounded by the given curves is 815π