Is it possible to determine the value for ${\int }_{-\pi /4}^{\pi /4}\sin (x^3)\mathrm{dx}$, if no calculators or computers can be used?
I would appreciate some help.
Thanks

Tony

Draw a rough sketch of the function, and recall that an integral can be interpreted as an area.

The answer to part one is that, since sin(-x)=
-sin(x), the graph of the fuction turns out to be odd and so the answer should be zero ( as negative areas will cancel out the positive one ). However, in case you aren't interested in negative areas, the integral turns out to be twice the integral of (sinx)^3 from 45 degrees to 0 degrees.

Thanks everyone.