   Chapter 13.2, Problem 34E ### 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

# In Problems 33-36, evaluate each integral (a) with the Fundamental Theorem of Calculus and (b) with a graphing calculator (as a check). ∫ 4 1 4 x + 5 x d x

(a)

To determine

To calculate: The value of the integral 144x+5xdx using Fundamental Theorem of Calculus.

Explanation

Given Information:

The provided integral is 144x+5xdx.

Formula used:

To calculate a definite integral, evaluate the indefinite integral and then substitute the limits of the integral.

The value of the integral xndx=xn+1n+1.

Fundamental Theorem of Calculus:

If f is a continuous function on a closed interval [a,b], then the definite integral of f exists and its value is abf(x)dx=F(b)F(a) where F is a function such that F(x)=f(x) for all x in [a,b].

Calculation:

Consider the integral 144x+5xdx.

Recall that to calculate a definite integral, evaluate the indefinite integral and then substitute the limits of the integral.

Thus, evaluate the integral.

Consider the expression (4x+5x).

Simplify the expression (4x+5x).

(4x+5x)=4xx+5x=4+5x=4+5x12

Thus, (4x+5x)=4+5x12.

Substitute 4+5x12 for (4x+5x) in 144x+5xdx.

Recall that if f is a continuous function on a closed interval [a,b], then the definite integral of f exists and its value is abf(x)dx=F(b)F(a) where F is a function such that F(x)=f(x) for all x in [a,b]

(b)

To determine

To calculate: The value of the integral 144x+5xdx using a graphing calculator.

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Rationalize the denominator: x12x.

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### Solve the equations in Exercises 126. 2(x21)x2+1x4x2+1x2+1=0

Finite Mathematics and Applied Calculus (MindTap Course List)

#### True or False: converges mean exists.

Study Guide for Stewart's Multivariable Calculus, 8th 