A level maths help!!

I have posted my working out so far for this integration by parts question, the worked solutions seem to rearrange the last part that I got up to in a way that I don't understand.

Could someone please explain?

(edited 1 year ago)

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Reply 1

ghostwalker

Original post by Idk131

If you call your initial integral I, then your last line is, I = something - 4I.
Rearrange to 5I = something, and I = (1/5) something.

(edited 1 year ago)

Reply 2

Idk131

Original post by ghostwalker

If you call your initial integral I, then your last line is, I = something - 4I.
Rearrange to 5I = someting, and I = (1/5) something.

thank you! Do you know if this is the only possible way to get to the final answer? Because I know that the spec for Edxecel would definately not require integration by parts for the 3rd time.

Reply 3

davros

Original post by Idk131

thank you! Do you know if this is the only possible way to get to the final answer? Because I know that the spec for Edxecel would definately not require integration by parts for the 3rd time.

You shouldn't be integrating by parts a 3rd time. The 1st time converts cos to sin and the 2nd time convers sin back to cos. So you end up with something like:

your integral = (some stuff) +(some multiple of your integral)

which you can rearrange to get: your integral = new multiple of "stuff"

This is the standard way of integrating e^(kx)cos(mx) or e^(kx)sin(mx) which you'll find in every calculus text :smile:

There is a "cheat" method that involves complex exponentials but I'm guessing that you're not doing FM, and even if you are there's still work to do to separate real and imaginary parts so it's not that much shorter than IBP!