Chapter 5 - Section 5.4 - The Fundamental Theorem of Calculus - Exercises - Page 322: 78

$1$

By the Fundamental Theorem of Calculus, the function $f(x)$ is the derivative of $\int_0^{x} f(t) dt=x \cos \pi x$ Thus, $f(x)=\dfrac{d}{dx} (\int_0^{x} f(t) dt)$ This implies that $\dfrac{d}{dx} (x \cos \pi x)=\cos \pi x- \pi x \sin \pi x$ Now, $f(4)=\cos 4 \pi- 4\pi \sin 4 \pi=1$