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# Maths at cam, warm up questions watch

1. Hi folks.

I'm just getting started with the work here and I'm beginning to think my gap year's taken its toll, as I can't wrap my head around a couple of 'warm up' questions for our first supervision . I think I'll get back into my stride eventually but for now I'd like to avoid looking a dunce in my first supervision if possible.

I don't necessarily want full solutions as I do want to be able to work these out myself, but I'd appreciate any hints or pointers.

Using integration by parts, show that

∫sechn+2u.sinhu.sinhu du = (n+1)-1∫sechnu du
(limits of integration between 0 and infinity)

I can't really see where the (n+1)-1 would come from in this.

And...

An = (qn / n!)∫[x(π-x)]nsinxdx
(limits of integration between 0 and pi)

Show that An = (4n-2)qAn-1 - (qπ)2An-2

Thanks again for any help. I don't have a whole lot to give but rep is available.

2. That's using x = cosh u. Use that result to get the first question.
3. Ah I see. I should've spotted that the 1/(n+1) might come from integrating something with a (n+1) power, so it was just a matter of finding a substitution that allowed me to integrate the multiple sech's.

Thanks AN, that worked a treat, rep on way as soon as I'm able to give it.

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Updated: October 8, 2006
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