Question

math

Answer 1

@Zepdrix

Answer 2

Remember how to do number 1?

Answer 3

yeah i did number one xD
i justneed help with 2- end number

Answer 4

\(\oint <\sin(x^{1/3}), x^3 + 3xy^2 > \cdot < dx, dy>\)

use Green, ie Stokes in \(\mathbb R^2\):

\( = \iint_A \det \begin{bmatrix} \partial_x & \partial_y \\
\sin(x^{1/3}) & x^3 + 3xy^2
\end{bmatrix} dA\)


\( = 3 \iint_A (x^2 + y^2) ~ dx~ dy\)

switching to polar...

\( \equiv 3 ~ \int\limits_{\theta = 0}^{2 \pi} ~ \int\limits_{r = 1}^{2} r^2 \cdot r ~dr ~d \theta\)

\( = 6 \pi \left[\dfrac{ r^4}{4}\right]_1^2 = \dfrac{ 45 \pi}{2}\)

Answer 5

how you know which theorem to use?

Answer 6

@Zepdrix

Answer 7

practice :)