Evaluate the integral by reversing the order of integration.

(2 integrals)
0 to 8
cube root(y) to 2 8e^(x^4) dx dy

1 answer

sketch the region. It will be clear that

∫[0,8] ∫[∛y,2] 8e^x^4 dx dy
= ∫[0,2] ∫[0,x^3] 8e^x^4 dy dx
= ∫[0,2] 8x^3 e^x^4 dx
= 2e^x^4 [0,2]
= 2(e^16-1)

Nice trick, since e^x^4 does not integrate well.