   Chapter 4.R, Problem 30E

Chapter
Section
Textbook Problem

# Evaluate the integral, if it exists. ∫ 0 4 | x − 1 |   d x

To determine

To evaluate:

04x-1 dx if it exists

Explanation

1) Concept:

By using Fundamental Theorem of calculus and rules of integration, evaluate the given integral.

2) Theorem:

Fundamental theorem of calculus:

If f is continuous on [a, b], then abfxdx=Fb-F(a).

3) Formula:

xndx=xn+1n+1+C

4) Given:

04x-1 dx

5) Calculation:

Consider, 04x-1 dx

x-1= -(x-1),       0x<1(x-1),       1<x4

x-1= (1-x),       0x<1(x-1),       1<x4

Since it is continuous in the given interval, the integral exists

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