What did I do wrong?
An object is formed so that its base is the quarter circle
y = sqrt(64 − x^2)
in the first quadrant, and its cross sections along the x-axis are squares. What is the volume of the object? (Assume the axes are measured in centimeters.)
I have already set up my equation as
1/64 * pi * r^2
r= 64 - x^2
limits of integration (0, 8)
For the integral, I have
pi/64 * integral from 0 to 8 of 64 - x^2 dx
I got pi/64 (64x - x^3/3)
That, evaluated at 8 gives me 34901/2083.
if you draw the square at x, it has a side of length 2y, or
2√(64-x^2)
So, the area of the square there is
4(64-x^2)
The volume is the sum of all those squares of thickness dx, so
v = ∫[0,8] 4(64-x^2) dx