Question

CHECK MY ANSWER! EASY CALC! The base of a solid in the xy-plane is the first-quadrant region bounded y = x and y = x2. Cross sections of the solid perpendicular to the x-axis are semicircles. What is the volume, in cubic units, of the solid?

Answer 1

Volume= Area * Thickness
dV= Area * Thickness
dV= 1/2(pi)r^2 * thickness
dV= 1/2(pi)r^2 * thickness
dV= 1/2(pi)r^2 * (y2-y1/2) dx
pi/8 (x-x^2)^2

intersection
x= x^2
1

pi/8 integral[0, 1] (x-x^2)^2
0.0131

Answer 2

@zepdrix

Answer 3

Ooo very nice! I think that's perfect.

Answer 4

I'm glad that you're thinking of it in terms of area and thickness and all that, most students just memorize the lazy formulas :)

Answer 5

Thanks! I have one more question I'm gonna have you check my answer. So stick around!

Answer 6

k cool