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
