Area In Exercises 83-86, use a graphing utility to graph the region bounded by the graphs of the equations. Then find the area of the region analytically.
To calculate: The area of the region bounded by the equations and also by the graphing utility method.
Given: given equations are
Here, we are Using “desmos” calculator to draw the graph of the bounded region.
Firstly, enter the given equations;
Since then, .
To Find the area of the bounded region
Now, in order to find the area of the bounded region with equations
Now, Substitute the value of
By Apply integration by part method.
Differentiating with respect to x
Now, by applying the formula for integration by part,
Then substitute the value of the function.
Again by appling the integration by part in the
Now, again by the use the formula for integration by part,
On Substituting the value of the integration in equation (1)
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