Chapter 4 - Integrals - 4.3 The Fundamental Theorem of Calculus - 4.3 Exercises - Page 327: 26

$10\pi$

Evaluate the integral: $\int^{5}_{-5}\pi dx$ Recall the 2nd part of the Fundamental Theorem of Calculus: $∫^b_af(x)dx=F(b)−F(a)$ Find $F(x)$: $F(x)=\int\pi dx$ $F(x)=\pi \int1dx$ $F(x)=\pi x$ (since $\pi$ is a constant it can be pulled out of the integral) Now evaluate $F(b)−F(a)$: $F(5)−F(-5)$ $5\pi- -5\pi$ $10\pi$