Rotate region bounded by given curves y= 7-x^2 by the x-axis when (x = -2, 2)?

1 Answer
Nov 29, 2017

#V=pi[2012/15]~~134.1picolor(white)(88)#cubic units

Explanation:

I am assuming you are asking for the volume when rotated about the x axis.

We first need to find the integral: #int_(-2)^(2)(7-x^2)^2 dx#.

Expanding #(7-x^2)^2#

#(7-x^2)^2=49-14x^2+x^4#

#V=piint_(-2)^(2)(49-14x^2+x^4) dx=49-14/3x^3+1/5x^5#

#V=pi[49-14/3x^3+1/5x^5]_(-2)^(2)#

#[49-14/3(2)^3+1/5(2)^5]-[49-14/3(-2)^3+1/5(-2)^5]#

#[1006/15]-[-1006/15]#

#->V=pi[2012/15]~~134.1picolor(white)(88)#cubic units