integrate cosx+sqrt(1+x^2)*sin^3x*cos^3x
where x is from pi/4 t pi/4
any idea? tooooo complicated... tks!
inte cosx+sqrt(1+x^2)*sin^3x*cos^3x (x from pi/4 t pi/4)

 Posts: 9
 Joined: Sat Oct 01, 2011 11:21 pm
Re: inte cosx+sqrt(1+x^2)*sin^3x*cos^3x (x from pi/4 t pi/4)
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..
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..
Re: inte cosx+sqrt(1+x^2)*sin^3x*cos^3x (x from pi/4 t pi/4)
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.
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.