Green's Theorem and Polar Coordinates for Circle Integration

[Titans86]

Homework Statement

F = [−y^3, x^3], C the circle x^2 + y^2 = 25

Book gives answer as Pi*1875*1/2, I get Pi*1875

The Attempt at a Solution

\int\int(3x^2 + 3y^2)dxdy

\int\int(75(cos^2\vartheta + sin^2\vartheta))rdrd\vartheta

75\int[1/2 r^2]^{5}_{0}d\vartheta

\frac{1875}{2}\intd\vartheta

[\frac{1875}{2}\vartheta]^{2\pi}_{0}

=1875\pi Where did I go wrong?

 

[rock.freak667]

When you have


<br /> \int\int(3x^2 + 3y^2)dxdy<br />

and then convert to polar coordinates x=rcos(theta) and y=rsin(theta)

r is not 5. r is a variable you are integrating.

 

[Titans86]

When you have


<br /> \int\int(3x^2 + 3y^2)dxdy<br />

and then convert to polar coordinates x=rcos(theta) and y=rsin(theta)

r is not 5. r is a variable you are integrating.

Of course! Thank you for the quick reply.
Regards,
Adam