Integration by Parts

[legacyofpiracy]

Hello, I actually have two problems I have questions on but I thought I would just begin with the easier of the two. Hopefully if I understand the solution to the first I should be able to figgure out the second.

Use integration by parts to evaluate the definite integral

  e
S    2(t^2)ln(6t)dt
  1

I am not quite sure how to begin or how I am to use the "e" and "1" limits. Any help would be greatly appreciated.

 

[stapel]

The limits are, as usual, just the values at which you'll be evaluating after integrating.

To "begin" an "integration by parts", you need to pick which part will be "u" and which will be "dv" (or "v" and "du", depending on your book). Then plug into the "integration by parts" formulation, and see if what you get is any simpler than what you started with.

Don't be worried if your first attempt looks messier than what you started with. This often happens, and is perfectly okay. If you don't like how the new integral looks, then try the "by parts" a different way. For instance, if you don't like "u = t² and dv = ln(6t) dt", then try "u = ln(6t) and dv = t² dt", and see if that works better for you.

Eliz.

 

[Unco]

Hello, I actually have two problems I have questions on but I thought I would just begin with the easier of the two. Hopefully if I understand the solution to the first I should be able to figgure out the second.

Use integration by parts to evaluate the definite integral

  e
S    2(t^2)ln(6t)dt
  1

I am not quite sure how to begin or how I am to use the "e" and "1" limits. Any help would be greatly appreciated.

A good guide I've seen at SOS is L.I.A.T.E, in order of which functions to choose for u: logs, inverse trigonometric, algebraic, trigonometric, exponential base e.

 

[legacyofpiracy]

Oh great! Thank you both for your help, I mannaged to get it allong with the second problem. Thanks again!