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**preview**shows half of the first page. to view the full**1 pages of the document.**11.10 Infinite Sequences & Series

Taylor & Maclaurin Series

Question #4 (Medium): Evaluating Indefinite Integral as Infinite Series

Strategy

Any given function inside the indefinite integral can be expressed as a infinite series. Then put that sum

expression inside the indefinite integral, then focus on the power of , since the integral is with respect

to variable . Then all else is treated as number, including the series counter , but power is raised by

, and that power needs to be offset by the reciprocal fraction, thus the outcome being similar series

expression with power raised to one more, and offsetting coefficient added to the series expression.

Remember to add the arbitrary constant factor of since it is indefinite integral.

Sample Question

Evaluate the indefinite integral as an infinite series.

Solution

First take the expression inside the indefinite integral and express as an infinite series.

Then to evaluate the indefinite integral, put this summation expression inside the integral:

. Remember add the arbitrary constant

factor of !

The radius of convergence is:

and

, then

. Therefore the radius of

convergence is

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