http://www.cubeupload.com/files/d01fa3capture.jpg

What is the equation of the rectangle under the curve? The curve is 3cos(x).

Printable View

- Jun 25th 2008, 04:39 PMMyungArea of a rectangle under a cosine curve?
http://www.cubeupload.com/files/d01fa3capture.jpg

What is the equation of the rectangle under the curve? The curve is 3cos(x). - Jun 25th 2008, 04:47 PMMathstud28
- Jun 25th 2008, 04:51 PMMyung
Is that all? My guess is 6xcos(x) because x+x times 3cos(x) with something like -pi/2 < x < pi/2 as the restrictions, is that incorrect?

- Jun 25th 2008, 04:56 PMMathstud28
- Jun 25th 2008, 05:00 PMMyung
I'm looking for an equation for the area of the rectangle inscribed under the curve 3cos(x) in the picture, the rectangle represents the dotted lines from -x to x. I don't really know where to start.

- Jun 25th 2008, 05:10 PMChris L T521
The Area of the rectangle is $\displaystyle A(x)=Base*Height=6x\cos(x)$

Are we supposed to find the value of x that maximizes the area?

Thus, $\displaystyle \frac{dA}{dx}=-6x\sin(x)+6\cos(x)$

Setting this equal to zero, we get that $\displaystyle \cot(x)=x$. Using your calculator, we see that this is the case for $\displaystyle x=\pm.86 \ x\in\left[-\frac{\pi}{2},\frac{\pi}{2}\right]$

We take the positive value.

Thus, the area of the rectangle is $\displaystyle A(.86)=6(.86)\cos(.86)\approx \color{red}\boxed{3.37}$.

I believe this is the answer.

Hope that this makes sense to you! :D

--Chris - Jun 25th 2008, 05:12 PMMathstud28
- Jun 25th 2008, 05:18 PMMyung