   Chapter 7.4, Problem 12E

Chapter
Section
Textbook Problem

# Evaluate the integral. ∫ 0 1 x − 4 x 2 − 5 x + 6   d x

To determine

To evaluate the integral 01x4x25x+6dx

Explanation

Calculation: Given 01x4x25x+6dx,

The denominator can be factored as

x25x+6=x23x2x+6=x(x3)2(x3)=(x2)(x3)

The partial fraction decomposition of the function is

x4x25x+6=x4(x2)(x3)=Ax2+Bx3x4=A(x3)+B(x2)x4=(A+B)x+(3A2B)Equating the coefficients of xandx0,we getA+B=1,3A2B=4on solving for AandB,we getA=2,B=1x4</

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