polar coordinated two variable calculus

• Feb 22nd 2009, 05:30 AM
James0502
polar coordinated two variable calculus
Using polar coordinates evaluate

int int over D 3(x+y) and D is x^2 + y^2 <=9, x>=0

Ok, I have

int (between -pi/2 and pi/2) d theta . int(between 3 and 0) 3r^2(costheta + sintheta)

giving 18

is this right?

it seems i'm missing something I think

many thanks
• Feb 22nd 2009, 09:44 AM
HallsofIvy
Quote:

Originally Posted by James0502
Using polar coordinates evaluate

int int over D 3(x+y) and D is x^2 + y^2 <=9, x>=0

Ok, I have

int (between -pi/2 and pi/2) d theta . int(between 3 and 0) 3r^2(costheta + sintheta)

giving 18

is this right?

it seems i'm missing something I think

many thanks

Although the integral, $\displaystyle 3\int_{\theta= -\pi/2}^{\pi/2} \int_{r= 0}^3 r^2(cos(\theta)+ sin(\theta) dr d\theta$ is correct, I do NOT get 18 for that integral. Could you show how you got that?
• Feb 22nd 2009, 09:57 AM
James0502
erm.. ok

integrate first wrt r - to give 9 (cos theta + sin theta) then wrt theta to give
9(sin theta - cos theta)

putting limits in gives 18

oh wait

i need to multiply by 3?