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MKNB

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[Fast Answer] Double Integral

Question:   Evaluate    i=(integral 0 to 4 ) integral (sqrty to 2)  y cox (x)^5 dx dy ?

Why we change dx and dy position and why cox(x)^5 does not solvable?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,649

Re: [Fast Answer] Double Integral

hi MKNB

Welcome to the forum.

This is not going to be easy.

Start with

When you expand the brackets the first two terms have the presence of a function and its derivative and so are directly integrable; the third is too.

That gives you a way to do the inner integral.

Then substitute y = u^2 and switch the outer integral to one involving du rather than dy.  It can be done in a similar way, converting the even powers of sine into cosines and using the function and its derivative method.

Worth switching the outer limits to u limits as the numbers convert easily too.

Good luck.  Let me know how you get on.

Later edit:

I gave this a try and the first part worked ok.  But the substitution didn't.  I've been out all day so haven't had a chance to try anything else.  I'll make a fresh post if I do.

Bob

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Children are not defined by school ...........The Fonz
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Sometimes I deliberately make mistakes, just to test you!  …………….Bob