Change of variables for double integral problem

[fuzzytoad]

Homework Statement

I want to use polar coordinates to integrate

1/sqrt(x^2+y^2) dydx with limits of integration 0 < y < x and 0 < x < 3

Homework Equations

x=rcosO
y=rsinO

The Attempt at a Solution

I know that the area being integrated over is the triangle enclosed by y=x and x=3. I have my limits for O to be 0 < O < pi/2, which I think is correct. I attempted to solve the problem using limits for r to be 3 < r < 3/cosO, however, the answer I obtain is 3(sqrt(2) - pi/2) whereas it should be 3ln(sqrt2 + 1). I think the problem is my limit for r.

Thanks in advance.

Edit: nevermind, I'm an idiot. Saw the problem right after I posted this.

 

[Mark44]

Homework Statement

I want to use polar coordinates to integrate

1/sqrt(x^2+y^2) dydx with limits of integration 0 < y < x and 0 < x < 3

Homework Equations

x=rcosO
y=rsinO

The Attempt at a Solution

I know that the area being integrated over is the triangle enclosed by y=x and x=3. I have my limits for O to be 0 < O < pi/2, which I think is correct. I attempted to solve the problem using limits for r to be 3 < r < 3/cosO, however, the answer I obtain is 3(sqrt(2) - pi/2) whereas it should be 3ln(sqrt2 + 1). I think the problem is my limit for r.

Thanks in advance.

Edit: nevermind, I'm an idiot. Saw the problem right after I posted this.

After converting to polar coordinates, your integral should be:
$$\int_{\theta = 0}^{\pi/4}\int_{r = 0}^{3sec(\theta)} \frac{r~dr~d\theta}{r}$$

Is that what you got?