Find the volume of the solid obtained by rotating the region bounded by y=10x and y=2x^2 around the x-axis.
+130544 Let's see where these curves intersect
10x = 2x^2
2x^2 - 10x = 0
2x ( x - 5) = 0 setting each factor to 0, the intersect points are x = 0 and x = 5
So we have
5
pi ∫ (10x)^2 - (2x^2)^2 dx =
0
5
pi ∫ 100x^2 - 4x^4 dx
0
5
pi [ 100x^3 / 3 - 4x^5/5] =
0
pi [ 100(5)^3/3 - 4(5)^5/5] = about 5235.99 cubic units
