Evaluating an Improper Integral In Exercises 7–20, determine whether the improper integral diverges or converges. See Example 1, 2, and 3.
To calculate: Whether the improper integral
Given Information:
The integral is provided as:
Formula used:
From definition of improper integral.
Also, the integral for the integration of a inverse function is as follows:
Calculation:
Consider the provided integral:
Use the property of improper integral
and simplify as:
Integrate the integrand by substation method as:
Assume
Differentiate as:
Now, substitute the values and integrate by using the inverse function formula
Again, substitute the value of
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