Answer
(a) $$\dfrac{3(\pi-3)}{2}$$
(b) $$-\dfrac{3\pi}{4}$$
Work Step by Step
(a) Work done$=\int_CF.dr$
$=\int_0^{1}(3ti+(-3t+3)j+\frac{\pi t}{2}k)(-3i+\frac{\pi }{2}j+3k)dt$
$=\int_0^{1}(-9t+3\pi/2)dt$
$=[-\dfrac{9t^2}{2}+\dfrac{3 \pi t}{2}]_0^{1}$
$=-\frac{9}{2}+\frac{3 \pi}{2}$
$=\dfrac{3(\pi-3)}{2}$
(b) Work done$=\int_CF.dr$
$=\int_0^{\pi/2}(3sinti+3costj+tk))(-3sinti+j+3costk)dt$
$=\int_0^{\pi/2}(-9sin^2t+3cost+3tcost)dt$
$=\frac{-9\pi}{4}+3+(\frac{3 \pi}{2}-3)$
$=-\dfrac{3\pi}{4}$
