Here is a line integral problem generated by
http://saab.org

Question

Here is a line integral problem generated by
http://saab.org

anonymous · Answer

attachment

ganeshie8 · Answer

connect 3pi/2 -> 2pi path, 

$\large  \mathbb{ \int_C -7x^{11}dx - 6x^{10}y dy = \oint -7x^{11}dx - 6x^{10}y dy - \int_C -7x^{11}dx - 6x^{10}y dy} $

ganeshie8 · Answer

will it work ? should i purse... or direct line integral will be easy ? hmm

ganeshie8 · Answer

Green's theorem for left loop :

$\large \mathbb{= \iint \limits_R -60x^9y ~ dA -  \int_C -7x^{11}dx - 6x^{10}y dy}   $

ganeshie8 · Answer

it seems to simplify... :)

ganeshie8 · Answer

$\mathbb{= \int_0^{2\pi} \int_0^1 -60\cos^9 t \sin t~ r dr dt -  \int_{3\pi/2}^{2\pi} -7\cos^{11}t (-\sin t dt) - 6\cos^{10} t \sin t (\cos t dt)}   $

ganeshie8 · Answer

$\large \mathbb{= 0 -  \int_{3\pi/2}^{2\pi} cos^{11}t \sin t dt}   $

ganeshie8 · Answer

$\large \mathbb{\frac{1}{12}} $

ganeshie8 · Answer

i feel direct line integral is also same complexity this time..

anonymous · Answer

@ganeshie8, I agree.

anonymous · Answer

Here is the solution generated by http://saab.org