   Chapter 5.1, Problem 4E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
5 views

# Integration and Differentiation In Exercises 1- 6, verify the statement by showing that the derivative of the right side is equal to the integrand on the left side. ∫ 4 x d x = 8 x + C

To determine

To prove: The verification of the statement (4x)dx=8x+C such that the derivatives of the right side is equal to the integrand on the left side.

Explanation

Given Information:

The provided indefinite integral is (4x)dx=8x+C.

Formula used:

Power rule of derivative is ddx(xn)=nxn1, where n is a real number.

Sum rule for function f(x)=u(x)+v(x), where f(x) and g(x) are differentiable functions of x, then ddx[f(x)+g(x)]=f(x)+g(x).

Proof:

Consider the indefinite integral (4x)dx=8x+C.

The left side integrand of the indefinite integral expression is (4x).

The right-side of the provided indefinite integral expression is (8x+C).

Differentiate the right-side term with respect to x, use the sum rule of differentiation ddx[f(x)+g(x)]=f(x)+g(x)

### 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

#### Solve the equations in Exercises 126. (x2+1)5(x+3)4+(x2+1)6(x+3)3=0

Finite Mathematics and Applied Calculus (MindTap Course List)

#### Prove the identity. 49. cot2 + sec2 = tan2 + csc2

Single Variable Calculus: Early Transcendentals, Volume I

#### In Problems 19-44, factor completely. 31.

Mathematical Applications for the Management, Life, and Social Sciences

#### True or False: n=1n+n3n2/3+n3/2+1 is a convergent series.

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

#### Determine A.

Mathematics For Machine Technology 