Question 23 ptsEvaluate the following integral between x=0and x=7:8х + x dx

Answered: Evaluate the following integral between…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Related questions

Question

Expert Solution

Step 1

Given

$\int 8 x^{3} + x d x$

Find : The value of the given integral between x=0 and x=7

Consider, $\int_{0}^{7} 8 x^{3} + x d x$

$\int_{0}^{7} 8 x^{3} + x d x$ = $8 \int_{0}^{7} x^{3} d x + \int_{0}^{7} x d x$

By using the formula $\int x^{n} d x = \frac{x^{n + 1}}{n + 1}$ , we get

$\int_{0}^{7} 8 x^{3} + x d x$ = $8 {[\frac{x^{3 + 1}}{3 +!}]}_{0}^{7} + {[\frac{x^{1 + 1}}{1 +!}]}_{0}^{7}$

= $8 {[\frac{x^{4}}{4}]}_{0}^{7} + {[\frac{x^{2}}{2}]}_{0}^{7}$

Applying the limit values , we get

= $8 [\frac{7^{4} - 0}{4}] + [\frac{7^{2} - 0}{2}]$

= $2 (2401) + [\frac{49}{2}]$

= $4802 + [\frac{49}{2}]$

= $\frac{2 (4802) + 49}{2}$

= $\frac{9653}{2}$

= 4826.5

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

Solve for the integral of the following functions.
Compute the following. (2x + 7)2 x 2 dx dx (2x + 7)2 %3D x 2 Enter your answer in the answer bOx.
finda y given that 2xy = 4 2 dx

Recommended textbooks for you

Calculus: Early Transcendentals

Calculus

ISBN:

9781285741550

Author:

James Stewart

Publisher:

Cengage Learning

Thomas' Calculus (14th Edition)

Calculus

ISBN:

9780134438986

Author:

Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher:

PEARSON

Calculus: Early Transcendentals (3rd Edition)

Calculus

ISBN:

9780134763644

Author:

William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher:

PEARSON

Calculus: Early Transcendentals

Calculus

ISBN:

9781285741550

Author:

James Stewart

Publisher:

Cengage Learning

Thomas' Calculus (14th Edition)

Calculus

ISBN:

9780134438986

Author:

Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher:

PEARSON

Calculus: Early Transcendentals (3rd Edition)

Calculus

ISBN:

9780134763644

Author:

William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher:

PEARSON

Calculus: Early Transcendentals

Calculus

ISBN:

9781319050740

Author:

Jon Rogawski, Colin Adams, Robert Franzosa

Publisher:

W. H. Freeman

Precalculus

Calculus

ISBN:

9780135189405

Author:

Michael Sullivan

Publisher:

PEARSON

Calculus: Early Transcendental Functions

Calculus

ISBN:

9781337552516

Author:

Ron Larson, Bruce H. Edwards

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS

Evaluate the following integral between x=0 and x=7: 8x + x dx