Chapter 4: Applications of Derivatives - Section 4.7 - Antiderivatives - Exercises 4.7 - Page 238: 11

a) $\cos \pi x+C$ b) $-3 \cos x+C$ c) $\dfrac{-1}{\pi} \cos \pi x+\cos 3x+C$

a) The anti-derivative is: $(-\pi)[ (\dfrac{-1}{\pi} \cos \pi x)]=\cos \pi x+C$ b) The anti-derivative is: Thus, we have $3( -\cos x)=-3 \cos x+C$ c) The anti-derivative is: Thus, we have $(\dfrac{-1}{\pi})\cos \pi x- 3(\dfrac{-1}{3} \cos 3 x) +C=(\dfrac{-1}{\pi}) \cos (\pi x)+\cos (3x)+C$