integrate help please
i love integrals, bring it on!
\[a \int\limits_{0}^{1} (dw)/(\sqrt{1-w ^{2}})\]
\[\int\limits_0^1 \left(\sqrt{1-w^2}\right) \, dw=\frac{\pi }{4} \]
and a work out would be helpful too
where does the pi come from
The indefinite integral is:\[\frac{1}{2} \left(w \sqrt{1-w^2}+\text{ArcSin}[w]\right)+C \]
let: w=sin(u) dw=cos(u) thus: int sqrt(1-sin^2(u))= cos u and u= sin^(-1)u thus: int cos^2(u) du = int 1/2 cos(2u)+1/2 du (double angle formula) do those two, and you'll arrive back at:... well what robtoey has, and plug and play from there.
we lost the a
lol didnt notice it... its a constant, so just put an a in the answer :P
i am still confused
Sorry. Overlooked "a" The answer is:\[a*\frac{ \pi }{4} \]
where is the trig functions coming from?
Refer to the tiff attachment from www.WolframAlpha through Mathematica 8.04 Home Edition.
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