[Multiple Integration] Integration of "xcos(xy)" with respect to dydx. The bounds are 0-1 for x. And 0-pi/2 for y.

I tried doing this, but I don't think I have the first integration right. From my understanding, the first "x" stays as is since I am integrating w.r.t dy first (constant). Cosine changes to sine. But integrating the inside (xy) part confuses me. Am I supposed to use u-sub?

In the second integral I think I have to use Itegration by Parts. I'm a bit rusty. Can someone help me?

Question

[Multiple Integration] Integration of "xcos(xy)" with respect to dydx. The bounds are 0->1 for x. And 0->pi/2 for y. 

I tried doing this, but I don't think I have the first integration right. From my understanding, the first "x" stays as is since I am integrating w.r.t dy first (constant). Cosine changes to sine. But integrating the inside (xy) part confuses me. Am I supposed to use u-sub? 

In the second integral I think I have to use Itegration by Parts. I'm a bit rusty. Can someone help me?

goformit100 · Answer

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amistre64 · Answer

$$\int\int xcos(xy)dydx$$
$$\int\left(\int xcos(xy)dy\right)dx$$
$$\int[\sin(xb)-\sin(xa)]dx$$
etc

amistre64 · Answer

sin(3y) derives to  3cos(3y) ... so assume x is a constant wrty