Convert polar coordinates to rectangular coordinates and evaluate integral

[jander]

I need help with a double integral.
I need to convert this double integral that is in polar coordinates to rectangular coordinates, then I need to evaluate the integral.

Integral[{0, Pi/2} Integral[{0, 2*a*sin(theta)} r*Sin(2*theta) dr d(theta)

 

[Deleted member 4993]

I need help with a double integral.
I need to convert this double integral that is in polar coordinates to rectangular coordinates, then I need to evaluate the integral.

Integral[{0, Pi/2} Integral[{0, 2*a*sin(theta)} r*Sin(2*theta) dr d(theta)

Substitute:

x = r * cos(Θ)

y = r * sin(Θ)

What are your thoughts?

Please share your work with us ...

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[HallsofIvy]

Have you learned to change the differentials? That is, change \(\displaystyle drd\theta\) into something involving dx and dy? You can find the "Jacobian" to do that.