# Thread: Area Between Curves

1. ## Area Between Curves

Let R be the region bounded by the graph of y =x ex cos(x), the origin and the line x = 2.

Sketch the graph of R. Show the scale.
Find the area of region R.

So far, I've tried to sketch the region and this is all I have. I'm not even sure if it's right.
Look at the link below, please.

Scriblink - Your Online Whiteboard

2. This is your function? $\displaystyle y = xe^x\cos x$

Does it intersect the x-axis on the interval $\displaystyle (0,2)$ ?

3. Yes.

4. Ok, now solve

$\displaystyle \int_{0}^{\frac{\pi}{2}}xe^x\cos x ~dx + \left|\int_{\frac{\pi}{2}}^{2}xe^x\cos x ~dx\right|$