## Thomas' Calculus 13th Edition

$\pi$
Formula to calculate the flow is given by: $\int_C F(r(t)) \dfrac{dr}{dt}(dt)$ Here, $\dfrac{dr}{dt}=- \sin t i+0j+\cos tk$ Now, $\int_0^{\pi}(- \sin t i+0j+\cos tk)((\cos t- \sin t) i+0j+\cos tk) dt= \int_0^{\pi}(\dfrac{-1}{2})( \sin 2t )+1 dt$ Thus, $[ (\dfrac{1}{4}) (\cos 2t) +t]_0^{\pi}=\pi$