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Mathematics 44 Online
OpenStudy (konradzuse):

Use Wallis's Formulas to evaluate the integral.

OpenStudy (konradzuse):

\[\int\limits_{0}^{\pi/2} (\sin(x))^5dx\]

OpenStudy (konradzuse):

according to the book it's the integral = \[\frac{2}{3}\frac{4}{5}\]

OpenStudy (konradzuse):

I guess that means it's = to 8/15?

OpenStudy (anonymous):

I'm not familiar with the formula you're talking about, but I think it's similar to\[\int(1-\cos^4x)\sin x\,dx\]or some such variation, where simple trig substitutions are used.

OpenStudy (konradzuse):

here I have attached it....

OpenStudy (konradzuse):

yup 8/15 works.

OpenStudy (anonymous):

I'm about to log out. @Ishaan94 Help please. :) I'm indebted to you.

OpenStudy (konradzuse):

:)

OpenStudy (lgbasallote):

@badreferences here's a tutorial on wallis' formula if you're interested :) http://openstudy.com/updates/4fa2341ae4b029e9dc332b3f

OpenStudy (konradzuse):

@lgbasallote so apparently I can use this whenever the integral is from 0 to pi/2? The next question is kinda hairy, so I figured this might be of use...

OpenStudy (konradzuse):

\[\int\limits_{0}^{\pi/2} \frac{\cos(t)}{19+\sin(t)}\]

OpenStudy (konradzuse):

\[\frac{1}{19}\int\limits_{0}^{\pi/2} \cos(t) \sin(t)^{-1}\]

OpenStudy (lgbasallote):

hmm you cant do that..

OpenStudy (konradzuse):

no? :(

OpenStudy (lgbasallote):

\[\frac{1}{19} \cos t \sin t ^{-1} = \frac{\cos t}{19\sin t}\]

OpenStudy (lgbasallote):

but good news is you can use u-sub :DDD u = 19 + sin t du = cos t dt

OpenStudy (lgbasallote):

so you use ln thingies

OpenStudy (konradzuse):

I don't wanna! :p

OpenStudy (konradzuse):

so I guess it's going to be ln|u| + c ln|19+sin(t)| + c for 0 to pi/2

OpenStudy (lgbasallote):

lol why is it so important to use wa;;os =)) and yup

OpenStudy (lgbasallote):

wallis*

OpenStudy (konradzuse):

cuz I wanted to be cool :P

OpenStudy (konradzuse):

\[\ln|19 + \sin(\pi/2)| - \ln|19\sin(0)|\]

OpenStudy (konradzuse):

\[\ln|20| - \ln|19| = \ln|1| = 0\]

OpenStudy (konradzuse):

@lgbasallote I guess I did something wrong :(.

OpenStudy (lgbasallote):

ln 20 - ln 19 is not ln 1

OpenStudy (konradzuse):

oh? haha :P

OpenStudy (lgbasallote):

ln (20 - 19) = ln 1 though

OpenStudy (konradzuse):

http://www.wolframalpha.com/input/?i=ln%7C20%7C+-+ln%7C19%7C wolfram says!

OpenStudy (konradzuse):

yay that works! :D ty :D

OpenStudy (anonymous):

Dang, I've never seen Wallis' formula before. I use reduction and substitution for these sorts of problems. Looking through all my textbooks, there isn't a single mention of Wallis either.

OpenStudy (konradzuse):

that sucks... I have Larson calculus 9th ed... I could send it to you if you want, it's a pdf.

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