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


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

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


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

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