can you help me with this double integral?

Question

$\int_{0}^{2} \int_{x}^{2} x \sqrt{1 + y^{3}} d y d x$ $int_0^2int_x^2x sqrt(1+y^3) dy dx$

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Answer 1 · 2018-06-09T19:28:52

Reverse the order of integration and evaluate $int_0^2 int_0^y xsqrt(1+y^3) \ dx \ dy$

The region has $x <= y <= 2$ and $0 <= x <= 2$ .

Here is a picture of the region:

enter image source here

We can re-describe the region as: $0 <= x <= y$ and $0 <= y <= 2$ .

So we can integrate

$int_0^2 int_0^y xsqrt(1+y^3) \ dx \ dy$