Find the integral of (cos^2(x))((cosxsin^2n+1)*(pi/2*sinx)+(sinxsin^2n+1)(pi/2*cosx)) from 0 to pi/2

- anonymous

Find the integral of (cos^2(x))((cosxsin^2n+1)*(pi/2*sinx)+(sinxsin^2n+1)(pi/2*cosx)) from 0 to pi/2

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- katieb

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- primeralph

Input it more clearly.

- anonymous

\[\int\limits_{0}^{\pi/2}\cos ^{2}x(\cos x \sin ^{2n+1}(\frac{ \pi }{ 2 }sinx)+sinxsin ^{2n+1}(\frac{ \pi }{ 2 }cosx))dx\]

- primeralph

Go Wolfram.

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## More answers

- anonymous

I don't have the first clue on how to use that

- primeralph

http://integrals.wolfram.com/index.jsp

- swissgirl

Wolfram sucks these days :(

- primeralph

How?

- swissgirl

Thats what happens with all these free awesome programs

- primeralph

Well, I don't think it even has CAS.
I don't use it though.

- swissgirl

Well if you wanna see the steps then you gotta have membership

- primeralph

Well, I'd expect them to do that.

- swissgirl

Ummm this is an annoying function. @Skip2mylou426 what r u currently studying?

- swissgirl

Wolfram was the best matrix calculator .........

- primeralph

was?

- primeralph

Think it's always been Matlab......

- swissgirl

Welll ya Dont have matlab. I used to have mathematica but my comp broke down so dont have it no more :(

- primeralph

@Skip2mylou426 I think the integral can't be evaluated easily because of the form sin(acos(b))

- primeralph

@swissgirl Yeah, if you're into coding, you'll fancy Matlab.

- swissgirl

I guess he went to the lou :)

- anonymous

I was trying to type that monstrosity into Wolfram. Epic fail. It didn't work at all.

- anonymous

http://www.wolframalpha.com/widgets/view.jsp?id=dc816cd78d306d7bda61f6facf5f17f7 This might help too

- swissgirl

OMG IK THAT

- swissgirl

It always happens to me

- primeralph

There is no free CAS engine...........unless you can hack.
Otherwise, get your pen and paper.

- swissgirl

wait let me try wolframming it for u

- anonymous

A little rusty on the calculus. I haven't taken calc in 3 or 4 years unfortunately

- swissgirl

What course are u taking now?

- primeralph

@swissgirl No point.
The integrand has the form of a switch variable 'n' which would leave the answer not numeric, but algebraic........which requires a CAS software.

- anonymous

It's called Problem Solving. It's a combination of every type of math course that could've possibly been taken.

- swissgirl

FUNNNNNN :)

- anonymous

haha not quite. He only gives us 1 point per problem solved. All work is required and 500 points are needed to get an A. Class has one month left (halfway done) and I have 178 points right now. KILL ME.

- primeralph

I don't see the point in putting that into an integral.
The integrand can be simplified though....it just looks ugly.

- primeralph

|dw:1372916840241:dw|

- primeralph

|dw:1372917002693:dw|

- primeralph

.........then you start using the identities......

- swissgirl

Ohhhh cooollll
Ya I shld have thought of cleaning it up by using identities :)

- primeralph

Yeah, I'm sure you'd have figured it out eventually.
It's just boring to look at.

- anonymous

so clean it up using identities, then plug in?

- anonymous

is that a square that cuts off at the end?

- swissgirl

Yes it is

- primeralph

|dw:1372917328459:dw|

- anonymous

thanks! think it'll be messy if I don't use identities first?

- primeralph

Well, depending on how much math you know, yes and no.
You might be able to notice the symmetry; and if you can't fiddle with it,

- anonymous

@primeralph love your picture

- anonymous

just thought i would point that out

- primeralph

@hobbs978
Thanks. Yours too. No homo.

- anonymous

I appreciate your help!

- primeralph

You're welcome.
Sorry I couldn't finish it; I'm kinda tired today.

- anonymous

It's ok, I wish I even remembered how to start it. I feel like a failure.

- swissgirl

hahaha dont feel like one
I took 2 semesters of stats earlier this yr and I cant remember pellet
Yesterday I was looking at a question and was totally blank. I felt like the biggest failure

- primeralph

It's funny how the system changes your words by itself.
We know what you meant to type instead of "pellet"........

- primeralph

@Skip2mylou426
http://www.sosmath.com/trig/Trig5/trig5/trig5.html

- anonymous

So after plugging everything in...I come up with a big fat zero...

- swissgirl

hahahahaha :D Just smile

- primeralph

Well, zero is an answer...in many cases.

- anonymous

I may have made a mistake. ugh. ok I'm going to attempt to draw this.. hold on

- anonymous

|dw:1372918536405:dw|

- anonymous

ok so the \[\cos(0)^3\] is going to be equal to one and then I end up with..

- primeralph

0

- anonymous

|dw:1372918796639:dw|

- anonymous

what about the n?

- primeralph

Still 0

- anonymous

Ok that's what I originally had. Sorry, don't hate me

- primeralph

No, I don't hate you. Stop bringing yourself down.
Sure you're an awesome student.

- anonymous

I'm trying, I really am, but this class is insanely hard. The hardest class in our program is Modern Algebra (which I took last semester), and I thought that was easier than this. I'm at a loss. I don't know what to do.

- swissgirl

Modern Algebra = Abstract Algebra?

- anonymous

Give or take. Our professor wrote the text for it

- primeralph

That's the sad part; when your course is customized.

- swissgirl

Ok that is a really hard course.

- swissgirl

Why is that sad?

- primeralph

Well, it means you can't find the answers elsewhere......since the professor made them up.

- swissgirl

hahahaha yaaaaaa
My abstract algebra course was customized too

- anonymous

Almost our whole department is like that. The worst thing is that the majority of our professors are research-based and suck at teaching.

- swissgirl

Like most profs out there who cant teach

- primeralph

I learned a long time ago to never expect a professor to teach well.
I just get the syllabus and do my thing.

- Jhannybean

Exactly...

- Jhannybean

Hmm.. @satellite73 perhaps?...

- anonymous

that's the issue with this class, he just gives you a bunch of problems with no material to work with

- primeralph

Get "Engineering Math by KA Stroud"
Then go to "Advanced Engineering Math" by anybody.......but Kreyszig........that'll be later because it doesn't explain easy.

- primeralph

........you can get them online for free.....if you know your way.........

- anonymous

I probably lack the necessary skills to do that. Can't hurt to try though

- swissgirl

Ya I only do free stuff. I got mathematica for free and all my textbooks in pdf formats

- Jhannybean

mathematica for free?....i hate you. I need to torrentthis.

- primeralph

@Skip2mylou426
The first book explains quite well. I've used it for HS students, so it should be cool.

- anonymous

I'll have to check it out soon. Thanks again for your help, I think I'm going to go die now :)

- primeralph

Stay safe.

- experimentX

\[ \frac{2 (1)_{n-1}}{\pi \left( \frac 3 2\right)_{n-1} }\]
http://mathworld.wolfram.com/PochhammerSymbol.html

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