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

[cathy_liping]

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]

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]

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.