Chapter 5 - Section 5.3 - The Fundamental Theorem of Calculus - 5.3 Exercises - Page 407: 26

$\int\limits_{-1}^1 x^{100} dx=\dfrac{2}{101}$

$\int\limits_{-1}^1 x^{100} dx$ This is a single term function. Integrate and use the second part of the fundamental theorem of calculus to get the result: $\int\limits_{-1}^1 x^{100} dx=\dfrac{1}{101}x^{101}\Big|_{-1}^{1}=\dfrac{1}{101}[(1)^{101}-(-1)^{101}]=...$ $...=\dfrac{1}{101}[1-(-1)]=\dfrac{1}{101}(2)=\dfrac{2}{101}$