   Chapter 4.2, Problem 49E

Chapter
Section
Textbook Problem

# If ∫ 0 9 f ( x ) d x = 37 and ∫ 0 9 g ( x ) d x = 16 , find ∫ 0 9 [ 2 f ( x ) + 3 g ( x ) ]   d x

To determine

To find:

The integral 092fx+3gxdx

Explanation

1) Concept:

Use the properties of the integral.

i) ab[fx+gx] dx=abfxdx+abgxdx

ii) abcfxdx=cabfxdx

2) Given:

09f(x)dx=37  and 09g(x)dx=16

3) Calculation:

By using the property (i), the given integral becomes

092f(x)dx+093g(x)dx

By using property (ii),

092f(x)dx+

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