A3 2009 gyak 1

1. Integrálja a

$v(x,y,z)=(\mathrm{sh}(y^2\mathrm{ch}\,x)+\sqrt[3]{x+y^3},z\,\mathrm{sh}\,(\cos y)+yz,z^5+y^2)$

vektormezőt az

$r(t)=(t^3,t,\sin t),\quad\quad t\in[0,2\pi]$

görbe mentén!

Mo.

r(t) = (3t²,1,cost)

$\int v \mathrm{d}r=\int \limits_0^{2\pi} 3t^2\mathrm{sh}(t^3)+3t^2\mathrm{ch}\,(2t^3)+\sin t\mathrm{sh}\,(\cos t)+t\sin t +\cos t \sin^5t+t^2\cos t\;\mathrm{d}t$