Explanation Given: The integral: ∫ 0 1 ∫ − x − x 2 x − x 2 ( x 2 + y 2 ) d y d x Formula Used: The following formula of multiple integration is used in order to find the value of the iterated integral: ∬ f ( x ) f ( y ) d x d y = ∫ ( ∫ f ( x ) f ( y ) d x ) d y Calculation: Convert the double integral into polar coordinates by substituting: x = r cos θ y = r sin θ d x d y = r d r d θ The limits of the provided double integral are: 0 ≤ x ≤ 1 − x − x 2 ≤ y ≤ x − x 2 The region bounded by these curves is shown below, Since y = x − x 2 , y = − x − x 2 , x = 0 , x = 1 , y 2 = x − x 2 r 2 sin 2 θ = r cos θ − r 2 cos 2 θ r 2 sin 2 θ + r 2 cos 2 θ = r cos θ r 2 = r cos θ On further simplification:, r 2 − r cos θ = 0 r ( r − cos θ ) = 0 r = 0 , r = cos θ As x = 0 r cos θ = 0 c o s θ × cos θ = 0 cos 2 θ = 0 cos θ = 0 θ = π 2 The corresponding limits in polar coordinates will be: − π 2 ≤ θ ≤ π 2 0 ≤ r ≤ cos θ It should be noted that the limits can also be found from the figure above

11th Edition

ISBN: 9781337604741

Author: Larson

Publisher: Cengage Learning

See similar textbooks

Videos

Question

Chapter 14.3, Problem 20E

To determine

To Calculate: What the value of the iterated integral by converting to polar coordinates will be.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.3, Problem 19E

Chapter 14.3, Problem 21E

Students have asked these similar questions

The bracket BCD is hinged at C and attached to a control cable at B. Let F₁ = 275 N and F2 = 275 N. F1 B a=0.18 m C A 0.4 m -0.4 m- 0.24 m Determine the reaction at C. The reaction at C N Z F2 D

The correct answer is C,i know that we need to use stokes theorem and parametrize the equations then write the equation F with respect to the curve but i cant seem to find a way to do it, the integral should be from 0 to 2pi but i might be wrongcould you show me the steps to get to 18pi

A 10-ft boom is acted upon by the 810-lb force as shown in the figure. D 6 ft 6 ft E B 7 ft C 6 ft 4 ft W Determine the tension in each cable and the reaction at the ball-and-socket joint at A. The tension in cable BD is lb. The tension in cable BE is lb. The reaction at A is ( lb) i + Ib) j. (Include a minus sign if necessary.)

Chapter 14 Solutions

Calculus Loose Leaf Bundle W/webassign

Ch. 14.1 - CONCEPT CHECK Iterated Integral Explain what is...Ch. 14.1 - Prob. 2E Ch. 14.1 - Question: Evaluate the integral: 0x(2xy)dy Ch. 14.1 - Evaluating an IntegralIn Exercises 310, evaluate...Ch. 14.1 - Evaluating an IntegralIn Exercises 310, evaluate...Ch. 14.1 - Evaluating an IntegralIn Exercises 310, evaluate...Ch. 14.1 - Evaluating an Integral In Exercises 3-10, evaluate...Ch. 14.1 - Evaluating an IntegralIn Exercises 310, evaluate...Ch. 14.1 - Evaluating an Integral In Exercises 3-10, evaluate...Ch. 14.1 - Evaluating an Integral In Exercises 3-10, evaluate...

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.

What the value of the iterated integral by converting to polar coordinates will be.

Solution Summary: The author explains how to calculate the value of the iterated integral by converting it to polar coordinates.

Videos

To Calculate: What the value of the iterated integral by converting to polar coordinates will be.

Want to see the full answer?

Chapter 14 Solutions