Question

Use Wallis's Formulas to evaluate the integral.

Answer 1

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

Answer 2

according to the book it's

the integral = \[\frac{2}{3}\frac{4}{5}\]

Answer 3

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

Answer 4

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.

Answer 5

here I have attached it....

Answer 6

yup 8/15 works.

Answer 7

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

Answer 8

:)

Answer 9

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

Answer 10

@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...

Answer 11

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

Answer 12

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

Answer 13

hmm you cant do that..

Answer 14

no? :(

Answer 15

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

Answer 16

but good news is you can use u-sub :DDD

u = 19 + sin t
du = cos t dt

Answer 17

so you use ln thingies

Answer 18

I don't wanna! :p

Answer 19

so I guess it's going to be ln|u| + c

ln|19+sin(t)| + c for 0 to pi/2

Answer 20

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

and yup

Answer 21

wallis*

Answer 22

cuz I wanted to be cool :P

Answer 23

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

Answer 24

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

Answer 25

@lgbasallote I guess I did something wrong :(.

Answer 26

ln 20 - ln 19 is not ln 1

Answer 27

oh? haha :P

Answer 28

ln (20 - 19) = ln 1 though

Answer 29

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

wolfram says!

Answer 30

yay that works! :D ty :D

Answer 31

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.

Answer 32

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