   Chapter 4.2, Problem 45E

Chapter
Section
Textbook Problem

# Use the results of Exercises 27 and 28 and the properties of integrals to evaluate ∫ 1 4 ( 2 x 2 − 3 x + 1 ) d x

To determine

To evaluate:

The integral 142x2-3x+1dx

Explanation

1) Concept:

Use the result of exercises 27 and 28 and the properties of integral.

i.

abx dx=b2-a22

ii.

abx2 dx=b3-a33

iii. abcdx=c(b-a), where c is any constant

iv. ab[fx+gx] dx=abfxdx+abgxdx

v. abcfxdx=cabfxdx

2) Given:

142x2-3x+1dx

3) Calculation:

By using property (iv),

142x2-3x+1dx=142x2dx-143xdx+141dx

By using property (v),

=214x2dx-314xdx+141dx

Now, apply concept (i), (ii), and (iii) on above step

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