   Chapter 4.5, Problem 84E

Chapter
Section
Textbook Problem

# The following exercise are intended only for these who have already covered Chapter 6. Evaluate the integral. ∫ 0 2 ( x − 1 ) e ( x − 1 ) 2 d x

To determine

To evaluate:

The given definite integral.

Explanation

1) Concept:

i) The substitution rule: for definite integral: If g'(x) is a continuous function on a,b  whose f is continuous on range of u=g(x), then  abfgxg'(x)dx=g(a)g(b)f(u)du. Here g(x) is substituted as u and then differentiation g(x)dx =du

ii)

exdx=ex+c

iii)

aafxdx=0

2) Given:

02x-1ex-12dx

3) Calculation:

The given integral is

02x-1ex-12dx

Here using the substitution method

Substitute x-12=u

Differentiating with respect to x

2x-1

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