inte cosx+sqrt(1+x^2)*sin^3x*cos^3x (x from -pi/4 t pi/4)

Forum for the GRE subject test in mathematics.
cathy_liping
Posts: 9
Joined: Sat Oct 01, 2011 11:21 pm

inte cosx+sqrt(1+x^2)*sin^3x*cos^3x (x from -pi/4 t pi/4)

Postby cathy_liping » Mon Oct 17, 2011 6:20 am

integrate cosx+sqrt(1+x^2)*sin^3x*cos^3x

where x is from -pi/4 t pi/4

any idea? tooooo complicated... tks!

yoyobarn
Posts: 80
Joined: Sun Dec 19, 2010 7:01 am

Re: inte cosx+sqrt(1+x^2)*sin^3x*cos^3x (x from -pi/4 t pi/4)

Postby yoyobarn » Mon Oct 17, 2011 6:39 am

hi, according to wolframalpha (http://www.wolframalpha.com/input/?i=in ... +to+pi%2F4),
the answer is 1.414.., which strongly suggests sqrt(2)?

I have no idea how to do the working though, probably some clever trigonometric identity may help..

yoyobarn
Posts: 80
Joined: Sun Dec 19, 2010 7:01 am

Re: inte cosx+sqrt(1+x^2)*sin^3x*cos^3x (x from -pi/4 t pi/4)

Postby yoyobarn » Mon Oct 17, 2011 7:31 am

oh ok...

I think the trick is the integral of the right hand side (sqrt(1+x^2)*sin^3x*cos^3x) is zero since it is an odd function.

hence the whole integral reduces to integrating cos x.

Best regards.




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