Chapter 8, Problem 10RE

### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336

Chapter
Section

### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336
Textbook Problem

# Find the area of the surface obtained by rotating the curve in Exercise 9 about the y-axis.

To determine

To find: The area of the surface obtained by rotating the curve about y-axis.

Explanation

Given information:

The function of the curve is y=âˆ«1x(tâˆ’1)dtâ€‰â€‰1â‰¤xâ‰¤16 (1)

The lower limit is 1 and the upper limit is 16.

The Fundamental Theorem of Calculus, Part 1 is shown below:

g(x)=âˆ«axf(t)dtâ€‰â€‰aâ‰¤xâ‰¤b

Here, the continuous function on the interval [a,â€‰b] is f and the function is g.

Condition for the theorem to be valid:

• If the function is continuous on the interval [a,â€‰b] and differentiable on (a,â€‰b) .
• Also for the continuous condition, g'(x)=f(x) .

Calculation:

Apply Fundamental Theorem of Calculus (Part 1) in Equation (1).

y'(x)=xâˆ’1dydx=xâˆ’1

The expression to find the area of the surface (S) obtained by rotating the curve about the y-axis is shown below:

S=âˆ«ab2Ï€x1+(dydx)2dx (2)

Here, the derivative of the function y is dydx , the lower limit is a, and the upper limit is b.

Substitute xâˆ’1 for dydx , 1 for a, and 16 for b in Equation (2)

### 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

#### 37. (a) Find and if and (b) For to exist, what restriction must satisfy?

Mathematical Applications for the Management, Life, and Social Sciences

#### Solve each equation. x4+81=0

Trigonometry (MindTap Course List)

#### True or False: These lines are skew:

Study Guide for Stewart's Multivariable Calculus, 8th

#### True or False: ln(a + b) = ln a + ln b.

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