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  Discussion about math, puzzles, games and fun.   Useful symbols: √ ∞ ≠ ≤ ≥ ≈ ⇒ ∈ Δ θ ∴ ∑ ∫ π -

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Topic review (newest first)

anonimnystefy
2012-10-08 11:02:37

Where can you get with the substitution x=(b-a)-a*cos(theta)?

bobbym
2012-10-08 08:06:24

Checking them now.

Yes, they are the same.

zetafunc.
2012-10-08 07:50:36

These two integrals are identical...

bobbym
2012-10-08 07:41:24

Hi;

Alpha has a time limit. I do not think those two integrals are the same so something is wrong somewhere.

zetafunc.
2012-10-08 07:29:30

Never mind, forget W|A, it is unable to solve the problem so I do not trust its solution.

zetafunc.
2012-10-08 07:26:16

Hmm, I am skeptical about that last line. According to W|A it is giving me a horrendous-looking solution.

zetafunc.
2012-10-08 07:16:10

"(i) Use the substitution x = 2 - cosθ to evaluate the integral

.

(ii) Show that, for a < b,



where

and
."

I have done the first part and got



which is correct (according to WolframAlpha). But the second part of the question confuses me. I have done this:

Let x = (b - a) - cosθ, then dx = sinθdθ

and I have ended up with this:



but I do not know where to go from here. Help would be appreciated.

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