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