# Thread: finding area enclosed by the curves

1. ## finding area enclosed by the curves

find the area of the regions enclosed by the given curves:

Given: y=6cos(5x), y=6sin(10x), x=0, x=pi/10

I drew the given curves and I did not understand what area the question wants me to find.

I was thinking just finding the area where the top function is 6sin(10x) and the bottom function is 6cos(5x) from where they first intersect after 0 to pi/10

is that right?

thank you

2. If $y_1(x) = 6\cos{5x}$ and $y_2(x) = 6\sin{10x}$, then the area between the curves is $\int_0^{\pi/10}|y_1(x)-y_2(x)|dx$

In order to compute that integral you need to find where the two curves intersect in the interval $[0, \pi/10]$, and then determine where $y_1 \geq y_2$ and where it's not.

$6\cos{5x}= 6\sin{10x} \Leftrightarrow 6\cos{5x} = 2\cdot 6\cos{5x}\sin{5x}$

3. I would think not.

Your challenge is to find the first intersection. What is your plan for that? You shold be able to find an exact result. No approximations!

Your other challenge is to find ALL the area - both pieces added together. The real test is to see if you can do this properly. If you get zero (0), you missed something important.