Integrateurmum
New member
- Joined
- Mar 13, 2015
- Messages
- 2
The question is to change this to polar co-ords and evaluate:
\(\displaystyle \displaystyle{ \int_{-2}^2 \,}\) \(\displaystyle \displaystyle{ \int_{-\sqrt{4\, -\, y^2\,}}^{\sqrt{4\, -\, y^2\,}} }\,\) \(\displaystyle \sin\left(x^2\, +\, y^2\right)\, dx\, dy\)
I have tried subbing x^2 +y^2=r^2 , multiplying it the Jacobian determinant and changing the limits to r *cos(theta) and -r*cos(theta) using x= r *cos(theta) &
y= r *sin(theta). But that doesn't give an answer with "pi" in it. I would appreciate hints on what is the right techinique to solve it, not detailed answer.
Thank you very much!
\(\displaystyle \displaystyle{ \int_{-2}^2 \,}\) \(\displaystyle \displaystyle{ \int_{-\sqrt{4\, -\, y^2\,}}^{\sqrt{4\, -\, y^2\,}} }\,\) \(\displaystyle \sin\left(x^2\, +\, y^2\right)\, dx\, dy\)
I have tried subbing x^2 +y^2=r^2 , multiplying it the Jacobian determinant and changing the limits to r *cos(theta) and -r*cos(theta) using x= r *cos(theta) &
y= r *sin(theta). But that doesn't give an answer with "pi" in it. I would appreciate hints on what is the right techinique to solve it, not detailed answer.
Thank you very much!
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