# Thread: Find maximum and draw the graph of S(x)=I|xcosx|dx from 0->3pi/2

1. ## Find maximum and draw the graph of S(x)=I|xcosx|dx from 0->3pi/2

Hi!

I am stuck with this excersice, which needs to be done by tomorrow.
Find maximum and draw the graph of S(x)=I|xcosx|dx from 0->s in the intervall [0,3pi/2]
I is integral....

Can someone help me get started?

Thanks.

2. Originally Posted by StefanO
Find maximum and draw the graph of S(x)=I|xcosx|dx from 0->s in the intervall [0,3pi/2] I is integral....
The problem is ill defined. For example:

$\displaystyle S(2)=\displaystyle\int|2\cos 2| d2$ ( what does this means? )

Possibly the function is:

$\displaystyle S(x)=\displaystyle\int_0^x|t\cos t| dt$.

Then:

$\displaystyle S'(x)=|x\cos x|$.

Regards.

Fernando Revilla

3. I believe that the function should be written S(s) (as opposed to S(x) ).

You need to first find the critical numbers in the given interval. To do this set the derivative of S equal to 0.

To compute the derivative of S you need to apply the second fundamental theorem of calculus which essentially says that "a derivative cancels out an integral." (Don't take this too literally though).

So $\displaystyle S'(s)=s\cos s$.

I hope this gets you started.