Integration....

[sialoproject]

(x^2sinx)/ (1+x^6) from -pie/2 to pie/2

I can't even start on this one... OTL.
I used online calculator and I got 1 for the answer, but I don't think its right.
is it u substitution?

 

[galactus]

First of all, never spell \(\displaystyle \pi\) as PIE.

Next, this integral is not meant to be brutally evaluated. It is merely a matter of observation.

Graph it and you can see. It is an odd function. What does this tell you?.

You're correct, 1 is not the solution.

 

[sialoproject]

First of all, never spell \(\displaystyle \pi\) as PIE.

Next, this integral is not meant to be brutally evaluated. It is merely a matter of observation.

Graph it and you can see. It is an odd function. What does this tell you?.

You're correct, 1 is not the solution.

its integration. we aren suppose to figure it out without the calculator. but if its an odd function , that means y =x? Even functions are symmetric to x axis so...

 

[galactus]

Yes, the reason you are not supposed to use a calcualtor is because it is an observation problem.

A function is odd when f(-x)=-f(x).

If you plug in -x for the x in the function, you get \(\displaystyle \frac{-x^{2}sin(x)}{1+x^{6}}\)

Thus, the area under the graph from \(\displaystyle -\frac{\pi}{2}\) to \(\displaystyle \frac{\pi}{2}\) is............