Chapter 13: Q. 41 (page 1004)

Evaluate each of the double integral in the exercise 37-54 as iterated integrals
$\int \int_{R} \sin (x + 2 y) d A W h e r e R = {(x, y) | 0 \leq x \leq π, 0 \leq y \leq \frac{π}{2}}$

Short Answer

Expert verified

The value of the integral is 0

Step by step solution

Given information

We are given that $\int \int_{R} \sin (x + 2 y) d A W h e r e R = {(x, y) | 0 \leq x \leq π, 0 \leq y \leq \frac{π}{2}}$

Use iterated integral

We have,

$\int_{0}^{\frac{π}{2}} \int_{0}^{π} \sin (x + 2 y) d x d y = \int_{0}^{\frac{π}{2}} \int_{0}^{π} (\sin x \cos 2 y + \sin 2 y \cos x) d x d y = \int_{0}^{\frac{π}{2}} {[- \cos x \cos 2 y + \sin 2 y \sin x]}^{π}_{0} d y = \int_{0}^{\frac{π}{2}} (\cos 2 y) d y = {[\frac{\sin 2 y}{2}]}^{\frac{π}{2}}_{0} = 0$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Evaluate each of the double integral in the exercise 37-54 as iterated integrals
$\int \int_{R} \sin (x + 2 y) d A W h e r e R = {(x, y) | 0 \leq x \leq π, 0 \leq y \leq \frac{π}{2}}$

Short Answer

Step by step solution

Given information

Use iterated integral

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Logic and Functions

Applied Mathematics

Discrete Mathematics

Probability and Statistics

Pure Maths

Study anywhere. Anytime. Across all devices.

Evaluate each of the double integral in the exercise 37-54 as iterated integrals∫∫Rsin(x+2y)dAWhereR={(x,y)|0≤x≤π,0≤y≤π2}

Short Answer

Step by step solution

Given information

Use iterated integral

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Logic and Functions

Applied Mathematics

Discrete Mathematics

Probability and Statistics

Pure Maths

Study anywhere. Anytime. Across all devices.

Evaluate each of the double integral in the exercise 37-54 as iterated integrals
$\int \int_{R} \sin (x + 2 y) d A W h e r e R = {(x, y) | 0 \leq x \leq π, 0 \leq y \leq \frac{π}{2}}$