Chapter 5: Q9P (page 247)

Question: $\int \int_{A} sinxdxdy$ where A is the area shown in Figure 2.8

Short Answer

Expert verified

The required solution is $\int \int_{A} sinxdxdy = 6$ .

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 over each rectangle individually:

$\int \int_{A} sinxdxdy = \int_{0}^{π / 2} sinxdx \int_{0}^{2} dy + \int_{π / 2}^{π} sinxdx \int_{0}^{4} dx = 2 {(- cosx)}_{0}^{π / 2} + 4 {(- cosx)}_{π / 2}^{π} = 6$

Therefore, the value is $\int \int_{A} sinxdxdy = 6$ .

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Question: $\int \int_{A} sinxdxdy$ where A is the area shown 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: $\int \int_{A} sinxdxdy$ where A is the area shown in Figure 2.8