can you help me with this double integral?

Question

#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#