Chapter 5: Q10P (page 247)

Question: $\int \int_{A} y d x d y$ where A is the area in Figure 2.8

Short Answer

Expert verified

The required solution is $\int \int_{A} ydxdy = 5 π$

Step by step solution

Defining the Area of integration.

A definite integral between two points can be used to find the area under a curve between two points.

Separating the area of integration.

Divide the integration region into two rectangles and integrate each one separately:

$\int \int_{A} ydxdy = \int_{0}^{π / 2} dx \int_{0}^{2} ydy + \int_{π / 2}^{π} dx \int_{0}^{4} ydy = \frac{π}{4} (4 - 0) + \frac{π}{4} (16 - 0) = 5 π$

Therefore, the value is $5 π$ .

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 Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Question: $\int \int_{A} y d x d y$ where A is the area in Figure 2.8

Short Answer

Step by step solution

Defining the Area of integration.

Separating the area of integration.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Waves Physics

Energy Physics

Fundamentals of Physics

Rotational Dynamics

Modern Physics

Nuclear Physics

Study anywhere. Anytime. Across all devices.

Question: ∫∫Aydxdywhere A is the area in Figure 2.8

Short Answer

Step by step solution

Defining the Area of integration.

Separating the area of integration.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Waves Physics

Energy Physics

Fundamentals of Physics

Rotational Dynamics

Modern Physics

Nuclear Physics

Study anywhere. Anytime. Across all devices.

Question: $\int \int_{A} y d x d y$ where A is the area in Figure 2.8