Transforming a Double Integral to a Single Integral

[gikiian]

Homework Statement

Use polar coordinates to change the following double integral to a single integral involving only the variable r.

Double-Integral( \sqrt{1+(x^{2}+y^{2})^{2} )

The x-y region is x^2 + y^2 = 4 in the first quadrant.

2. The attempt at a solution
I got upto this:
Integral(pi/2 sqrt.(1+r^4) r dr)

Did I do it right?

 

[tiny-tim]

hi gikiian!

what are the given limits of integration in the question?

 

[gikiian]

The x-y region is x^2 + y^2 = 4 in the first quadrant. Thanks for reminding :)

 

[tiny-tim]

The x-y region is x^2 + y^2 = 4 in the first quadrant.

ah, thought so!

in that case, yes your integral is correct

(though showing a bit of working might have been a good idea )

 

[gikiian]

Hmm, thanks. Next time for sure :)

Now, evaluating the integral is a headache!

 

[tiny-tim]

(have a square-root: √ and try using the X² tag just above the Reply box )

try the simplest possible substitution