- #1

toforfiltum

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## Homework Statement

Transform given integral in Cartesian coordinates to one in polar coordinates and evaluate polar integral.

##\int_{0}^3 \int_{0}^x \frac {dydx}{\sqrt(x^2+y^2)}##

## Homework Equations

## The Attempt at a Solution

I drew out the region in the ##xy## plane and I know that ##0 \leq \theta \leq \frac{\pi}{4}##.

For ##r##, I thought that it should be ##3 \leq r \leq 3\sqrt 2##

So my polar integral is ##\int_{0}^ \frac{\pi}{4} \int_{3}^{3\sqrt 2} \frac{1}{\sqrt(r^2)} r drd\theta##.

The answer I get from this integral is ##\frac{3\pi}{4} (\sqrt2 -1)##

But the answer is ##3 \ln(\sqrt2+1)##.

I have no idea how ##ln## appears in the answer.

Where am I wrong?

Thanks!