$\"\"$

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The integral is $\"\"$ .

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$\"\"$

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$\"\"$ where $\"\"$ is $\"\"$ .

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So the above in equality is $\"\"$ .

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The function $\"\"$ increasing over the interva $\"\"$ .

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Consider the value of $\"\"$ is $\"\"$ .

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So the value of $\"\"$ is $\"\"$ .

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$\"\"$ .

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$\"\"$

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Comparison theorem :

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Suppose that $\"\"$ and $\"\"$ are continuous functions with $\"\"$ for $\"\"$ ,

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1. If $\"\"$ is convergent, then $\"\"$ is convergent.

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2. If $\"\"$ is divergent, then $\"\"$ is also divergent.

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Here $\"\"$ and $\"\"$ .

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$\"\"$

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Let $\"\"$ then $\"\"$ .

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$\"\"$

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Substitute corresponding values in above equation.

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$\"\"$

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Substitute $\"\"$ in the above equation.

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$\"\"$

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Since $\"\"$ is a finite value, it is convergent.

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Thus, $\"\"$ is convergent.

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$\"\"$

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$\"\"$ is convergent.