Answer
a) $\sin \pi x+C$
b) $\sin \dfrac{\pi x}{2}+C$
c) $\dfrac{2}{\pi} \sin \dfrac{\pi x}{2}+\pi \sin x+C$
Work Step by Step
a) The anti-derivative is:
$\pi (\dfrac{1}{\pi} \sin \pi x)+C=\sin \pi x+C$
b) The anti-derivative is:
$\dfrac{\pi}{2}\dfrac{1}{\pi/2} \sin \dfrac{\pi x}{2}+C=\sin \dfrac{\pi x}{2}+C$
c) The anti-derivative is:
$\dfrac{1}{\pi/2} \sin \dfrac{\pi x}{2}+\pi \sin x+C=\dfrac{2}{\pi} \sin \dfrac{\pi x}{2}+\pi \sin x+C$
