Question

Hope I didn't make any mistakes.
\[\int_c cosydx+x^2sinydy\]
C is the rectangle with vertices (0,0),(5,0),(5,2) and (0,2)
\[p=cosy\]
\[\frac{dp}{dy}=-siny\]
\[q=x^2siny\]
\[\frac{dq}{dx}=2xsiny\]
\[\int\int_R (2xsiny+siny)dxdy\]
\[\int_0^2\int_0^5(2xsiny+siny)dxdy\]
\[\int_0^2[x^2siny]_0^5dy\]
\[\int 25sinydy\]
25[-cos(2)+cos(0)]

Answer 1

just a little mistake in integrating for x i think...

Answer 2

are you using green's theorem ?? i guess .

Answer 3

yes Greens theorem

Answer 4

It should have been dydx?

Answer 5

C is a rectangle...it does'nt matter to write dydx or dxdy

Answer 6

my first integration is wrong?

Answer 7

a little mistake

\[\int\limits (2x \sin y+\sin y )dx = \sin y (x^2+x) +A\]

Answer 8

so in the last integral for y that will be ...30 sin y ... instead of ...25 sin y...

Answer 9

yes mukusha did figure out after first integration and application of limit you should have
30\[30\int\limits_{0}^{2}\sin(y)dy\]

Answer 10

Oh ok. Thank you guys!

Answer 11

yw :)

Answer 12

yw:)

Answer 13

it's perfect. I don't see any errors in it. :X