Question

Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis. y = x3/2, y = 8, x = 0

Answer 1

solve for the value of x such that f(x)=8
imma assume it is y=x^(3/2)
so
solve 8=x^(3/2)
x=4
so integrate from x=0 to x=4

`\pi \int\limits^4_0 {(x^ (3)/(2))^2 } \, dx` is the area

`\pi \int\limits^4_0 {x^3 } \, dx`=

`\pi [ (1)/(4)x^4 ]^4_0`=

`\pi (4^3)`=
64π cubic units