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Use the given transformation to evaluate the integral.

0 votes

Use the given transformation to evaluate the integral.

where R is the region bounded by the ellipse

asked Feb 18, 2015 in CALCULUS by anonymous
reshown Feb 18, 2015 by goushi

1 Answer

0 votes

Step 1 :

Change of variable in double integral :

Conversion of integral from rectangular to polar co-ordinates :

Step 2 :

The integral is image and the change of variables .

Where R  is the region bounded by the ellipse .

Substitute and in above equation.

Since the domain is a unit circle, the limits of integral are and

Find the Jacobian :

 

Step 3 :

 Evaluate the integral :

image

Write the above integral in polar co-ordinates :

Substitute and .

Since the domain is a unit circle, the new limits are and .

Solution :

answered Feb 24, 2015 by Thomas Apprentice
edited Feb 24, 2015 by Thomas

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