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 $5 π$ .

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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.

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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

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