   Chapter 7.4, Problem 55E

Chapter
Section
Textbook Problem

# Use a graph of f ( x ) = 1 / ( x 2 − 2 x − 3 ) to decide whether ∫ 0 2 f ( x )   d x is positive or negative. Use the graph to give a rough estimate of the value of the integral and then use partial fractions to find the exact value.

To determine

To Find: Use a graph of f(x)=1(x22x3) to decide whether 02f(x)dx is positive or negative. Use the graph to give a rough estimate of the value of the integral and then use partial fractions to find the exact value

Explanation

Calculation: From the graph below, we see that

021x22x3dx<0

021x22x3dx0.6

Note that x22x3=(x3)(x+1), and using a partial fraction decomposition we obtain

021x22x3dx=1402(1x31x+1)dx=14[ln|x3|l

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