(a) Explanation Given information: The curve is x = e 2 y , 0 ≤ y ≤ 2 . Formula used: The surface area formula with respect to x is given by S = 2 π ∫ a b x 1 + y ' 2 d x , when the rotation is about the y -axis. Calculation: Rewrite the equation in the form y = f x . x = e 2 y ln x = ln e 2 y ln x = 2 y y = ln x 2 The limits of variable x are: When y = 0 , x = 1 and, when y = 2 , x = e 4 . To set up the integral with respect to x for the area of the resulting surface of the curve x = e 2 y , 0 ≤ y ≤ 2 rotated about the y -axis, find the y ' = d y d x (b) To determine To find: The integral for the area of the resulting surface of the curve rotated about the y -axis by integrating the curve with respect to y -axis.

9th Edition

ISBN: 9781337613927

Author: Stewart

Publisher: CENGAGE L

See similar textbooks

Concept explainers

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence t…

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.

Videos

Question

Chapter 8.2, Problem 8E

(a)

To determine

To find: The integral for the area of the resulting surface of the curve rotated about the y -axis by integrating the curve with respect to x -axis.

(b)

To determine

To find: The integral for the area of the resulting surface of the curve rotated about the y -axis by integrating the curve with respect to y -axis.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.2, Problem 7E

Chapter 8.2, Problem 9E

Students have asked these similar questions

Graphically, explain the various forms of linear functions

2. Find the Bezier surface equation using the 9 control points shown below. Use the u and v directions shown. It is required to show all the calculation processes for finding Bernstein polynomials. Find the surface tangent, twist and normal vectors at point u=0.5 and v=0.5. (40 points) y 10 9 8 7 6 5 4 3 2 Poo и 1 1 2 3 4 5 6 7 8 9 10 10 X

A cable runs along the wall from C to P at a cost of $24 per meter, and straight from P to M at a cost of $26 per meter. If M is 10 meters from the nearest point A on the wall where P lies, and A is 72 meters from C, find the distance from C to P such that the cost of installing the cable is minimized and find this cost. C 72 P A 10 M

Chapter 8 Solutions

Calculus, Early Transcendentals

Ch. 8.1 - Use the arc length formula (3) to find the length...Ch. 8.1 - Use the arc length formula to find the length of...Ch. 8.1 - Set up, but do not evaluate, an integral for the...Ch. 8.1 - Set up, but do not evaluate, an integral for the...Ch. 8.1 - Set up, but do not evaluate, an integral for the...Ch. 8.1 - Set up, but do not evaluate, an integral for the...Ch. 8.1 - Set up, but do not evaluate, an integral for the...Ch. 8.1 - Set up, but do not evaluate, an integral for the...Ch. 8.1 - Find the exact length of the curve. 9....Ch. 8.1 - Find the exact length of the curve. 10....

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The integral for the area of the resulting surface of the curve rotated about the y -axis by integrating the curve with respect to x -axis.

Solution Summary: The author explains how to find the integral for the area of the resulting surface of a curve rotated about y axis by integrating the curve with respect to x.