   Chapter 10.2, Problem 63E

Chapter
Section
Textbook Problem

Find the exact area of the surface obtained by rotating the given curve about the x-axis.63. x = a cos3θ, y = a sin3θ, 0 ≤ θ ≤ π/2

To determine

To find: The surface area of the curve for the parametric equation x=acos3θ and y=asin3θ.

Explanation

Given:

The parametric equation for the variable x is as below.

x=acos3θ

The parametric equation for the variable y is as below.

y=asin3θ

The value θ ranges from 0 to π2.

Calculation:

The surface area of the surface obtained by rotating curve about the x axis is as below.

S=0π22πy(dxdθ)2+(dydθ)2dθ

The value θ ranges from 0 to π2.

Differentiate the variable x with respect to θ.

dxdθ=3asinθcos2θ

Differentiate the variable y with respect to θ:

dydθ=3acosθsin2θ

Write the length of the curve formula.

S=0π22πy(dxdθ)2+(dydθ)2dθ

Substitute (3asinθcos2θ) for dxdt and (3acosθsin2θ) for dydt in the above equation

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

Expand each expression in Exercises 122. (2x3)2

Finite Mathematics and Applied Calculus (MindTap Course List)

Absolute Value Evaluate each expression. 71. (a) | ( 2) 6| (b) (13)(15)

Precalculus: Mathematics for Calculus (Standalone Book)

In Exercises 6372, evaluate the expression. 66. |0.21.41.62.4|

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

3. Name the two major categories of life insurance. (19-1)

Contemporary Mathematics for Business & Consumers

[Type text] 2. If and ,are and are inverses? [Type text]

Mathematical Applications for the Management, Life, and Social Sciences

Write the sum in sigma notation. 16. 1+3+5+7++(2n1)

Single Variable Calculus: Early Transcendentals

True or False:

Study Guide for Stewart's Multivariable Calculus, 8th

If f(x) 5 for all x [2, 6] then 26f(x)dx. (Choose the best answer.) a) 4 b) 5 c) 20 d) 30

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