Chapter 4 - Integrals - 4.3 The Fundamental Theorem of Calculus - 4.3 Exercises - Page 327: 20

$\frac{2}{101}$

Evaluate the integral: $\int^1_{-1} x^{100} dx$ Recall the 2nd part of the Fundamental Theorem of Calculus: $\int_a^bf(x)dx = F(b) - F(a)$ Find $F(x)$: $F(x) = \int x^{100}dx $ $F(x) = \frac{x^{101}}{101}$ Now evaluate $F(b) - F(a)$: $F(1) - F(-1)$ $\frac{1^{101}}{101} - \frac{-1^{101}}{101}$ $\frac{1}{101} -\frac{-1}{101}$ $\frac{2}{101}$