##### Questions

##### Question type

Use these controls to find questions to answer

Featured 3 months ago

We have,

Featured 3 months ago

Visual: Check out this graph

We clearly cannot evaluate this integral as it is using any of the regular integration techniques we've learned. However, since it is a definite integral, we can use a MacLaurin series and do what is called term by term integration.

We'll need to find the MacLaurin series. Since we don't want to find the nth derivative of that function, we'll need to try and fit it into one of the MacLaurin series we already know.

Firstly, we don't like

So we have:

Why do we do this? Well, now notice that

...for all

So, we can use this relationship to our advantage, and replace

Evaluating the integral:

Cancelling out the

And now, we take the definite integral we began the problem with:

**Note**: Observe how we now do not need to worry about dividing by zero in this problem, which is an issue we'd have had in the original integrand due to the

Make sure you realize, though, that this series is only good on the interval

Hope that helped :)

Featured 3 months ago

The mass is obtained by calculating

Featured 3 months ago

Simplify the function:

so for

while for

Featured 2 months ago

Featured 1 month ago

=

=

and then

=

Ask a question
Filters

Ã—

Use these controls to find questions to answer

Unanswered

Need double-checking

Practice problems

Conceptual questions