Convert triangle vertices to double integral polar coordiantes

[ramses07]

Homework Statement

integrate

f(x,y) = sqrt(x^2+y^2)

over triangle with vertices (0,0) (0,sqrt2) (sqrt 2, sqrt 2)

Homework Equations

x= rcosO, y = rsinO

x^2+y^2=r^2

The Attempt at a Solution

im supposed to use a double integral converted to polar coordinates,
so i used the bounds int. 0 to pi/4 int. 0 to sqrt 2 sec (r^2) drdO

are these the correct bounds? because i can't seem to find the answer.

 

[cragar]

I think your bounds for theta should be pi/4 to pi/2

 

[ramses07]

how do you know what the bounds are?

 

[cragar]

because the line y=x cuts it at a 45 degree angle and x=0 goes up to 90 so it goes from 45 to 90
like cutting a wedge out of a circle , but the radius is different , i think your bounds for the radius are correct.