Please help thanks!

Question

Sketch the region in the first quandrant enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region.

y=2cos(x),    y=10sin(2x),   x=0

Answer 1

I will help you set up the problem.

 

Integrate along the x- direction from x = 0 to x =a, where 'a' is the value of x that solves the equation

 

5sin(2x) = cos(x)

 

sin(2x) = 2sinx cosx -- did I get this right?

 

So,  10sinx cosx = cos x 

or sinx = 1/10.

 

You can compute the arcsin or just say arcsin(1/10) is approximately 1/10.

 

This means the integration on x goes from x = 0 to x = 1/10.

The function integrated in

 

(2cosx - 10sin(2x)). You can finish this up

 

Nee