(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the area of the region enclosed between y=4sin(x) and y=2cos(x) from x=0 to x=0.8pi.

2. Relevant equations

[itex]\int^{0.8\pi}_0 dx [/itex]

[itex]

g(x) = 4\sin(x)

[/itex]

[itex]

f(x) = 2\cos(x)

[/itex]

3. The attempt at a solution

This problem needs to be split up into two parts.

[itex]

\int_0 ^n [f(x) - g(x)] dx + \int_n^{0.8\pi} [g(x) - f(x)] dx

[/itex]

My major problem is finding n.

I set:

[itex]

f(n) = g(n) \rightarrow 4\sin(n) = 2 \cos(n) \rightarrow 2\sin(n) = cos(n) \rightarrow 2 = \frac{cos(n)}{sin(n)} \rightarrow 2 = \cot(n)

[/itex]

I'm having trouble finding that point n. I've worked out that it's near

[itex]

\frac{15\pi}{96} = n

[/itex]

and with that n I have:

[itex]

\int_0^n [2 \cos(x) - 4 \sin(x)] dx + \int_n^{0.8\pi} [2 \cos(x) - 4\sin(x)] dx

[/itex]

[itex]

-2 \sin(x) - (-4) \cos(x)]_0^\frac{15\pi}{96} + [-2 \sin(x) - (-4) \cos(x)]_\frac{15\pi}{96}^{0.8\pi}

[/itex]

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# Homework Help: Area between two graphs

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