# Question #ae4f3

##### 1 Answer

The volume is

#### Explanation:

There is only one curve being rotated, so we can use the disc method. The disc method says that for each value of

#V = int_a^b pi*f(x)^2 dx = pi* int_a^b f(x)^2 dx#

First, we need to find our bounds. Since we are given no other bounds, the bounds must be the zeroes of

#0 = 4-4x^2#

#4x^2 = 4#

#x^2 = 1#

#x = +-1#

So, our bounds are

Now, all we have left to do is use the disc method formula to find the volume.

#V = pi* int_a^b f(x)^2 dx#

#= pi * int_-1^1 (4-4x^2)^2 dx#

#= pi * int_-1^1 4^2 * (1-x^2)^2 dx#

#= 16pi * int_-1^1 (x^4 - 2x^2 + 1) dx#

#= 16pi * (x^5/5-2x^3/3+x)|_-1^1#

#= 16pi * ((1/5 - 2/3+1) - (-1/5 + 2/3-1))#

#= 16pi * (2/5-4/3+2)#

#=(256pi)/15#

#= 53.617#

*Final Answer*