Finding Area with Double Integral In Exercises 45–48, use a double integral to calculate the area denoted by
To calculate: The area denoted by the expression
Given Information:
The provided expression and the equations are
Formula used:
To determine the area in the plane by double integrals mostly two kind of strips are used.
1. Vertical strip: In case of vertical strip shown below the region bounded is given by,
And the area of the region is given by,
2. Horizontal strip: In case of horizontal strip shown below the region bounded is given by,
And the area of the region is given by,
Calculation:
Consider the expression
First sketch the graph of region R which is bounded by the equations
The graph of the equation
For equation
For
For
For
For
Now construct a table showing different values of x and y as,
x | |
0 | 4 |
1 | 6 |
2 | 8 |
3 | 10 |
Thus the graph of the equation
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