   Chapter 13.2, Problem 26E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Evaluate the definite integrals in Problems 1-32. ∫ 0 2 e 4 x − 3 d x

To determine

To calculate: The value of the integral 02e4x3dx.

Explanation

Given Information:

The provided integral is 02e4x3dx.

Formula used:

If f is a continuous function on the closed interval [a,b], then the value of the definite integral of f that exists on the interval is,

abf(x)dx=F(b)F(a)

Where F(x)=f(x) for all x in closed interval [a,b].

Integral formula,

exdx=ex+C

Calculation:

Consider the provided integral 02e4x3dx.

Let the expression

(4x3)=u.

Differentiate with respect to x.

d(4x3)=du4dx=du

So, 4dx=du

Multiply and divide the numerator by 4 and rewrite the provided integral as

02e4x3dx=02e4x3×44dx=1402e4x3×4dx

Now, substitute the values in terms of u and du and simplif

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