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Calculus/Double Angel

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Expert: - 9/10/2008


Question
Well.. I've never asked an online question before, but this is due by midnight and I really need help. My problem is y=3cos(5x), y=3sin(10x), x=0, x= pi/10 find the area S of the region.

I know I have to use double angle formula, but that is all for sin(2x), etc
If you could help me, I would really really really appreciate it. Thanks :)

Answer
Welcome to the land of PC service.  Not only that, this service is free (that's unusual).

If we are going from x=0 to π/10 on the first equation, we are looking at the cos(x) from 0 to π/2, which is know to be concave down from 1 to 0.  The 3 out front means that is goes from 3 down to 0.

On the second equation, 3sin(10x), with x going from 0 to π/10, we are looking at sin(x) from 0 to π.  Sin(x) goes from 0 to 0 and has a maximum 1 in the middle.  Since it is 3sin(x), it goes from 0 to 0 with a maximum of 3 in the middle.  Note that this curve is also concave down.

Do you know what concave means?  Have you had calculus?

f(x)=x² is concave up and f(x)=-x² is concave down.

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