Question

evaluate the double integral
∫R∫ ye^x^3 dA

for the region R is bounded by x=y/2, x=1, and y=0
Just plug and chug:

∫[0,1]∫[0,2x] ye^x^3 dy dx
=∫[0,1] (1/2 y^2 e^x^3)[0,2x] dx
=∫[0,1] (1/2 4x^2 e^x^3) dx
= ∫[0,1] 2x^2 e^x^3 dx
= ∫[0,1] 2/3 e^x^3 d(x^3)
= 2/3 e^x^3[0,1]
= 2/3(e^1 - e^0)
= 2/3(e-1)

Related Questions

1. Evaluate the given integral by making an appropriate change of variables, where R is the region i... Evaluate double integral ln((x-y)/(x+y)) dy dx where the double integral region is the triangle with... Evaluate the double integral (x-y) dxdy over D, where D is where D is the region above the x axis an...