Hi, I was wondering if someone can help me complete this multi-step problem. The parts I've done are in **blue**. I'll post the whole of it, first (sorry, I don't know how to post an image of the curve):

The curve above is drawn in the xy-plane and is described by the equation in polar coordinates r = θ + sin(2 θ) for 0 ≤ θ ≤ π, where r is measured in meters and θ is measured in radians. The derivative of r with respect to θ is given by dr/dθ = 1 + 2cos(2θ).

a) find the area bounded by the curve and the x-axis.

So, for this, the area formula would be **1/2 ****∫ r^2 d****θ**, no? So it would end up being:

*1/2 ∫( θ + sin(2 θ) )^2, from 0 to pi, which yields? *

b) find the angle θ that corresponds to the point on the curve with x-coordinate -2.

?

I thik it means that since **x = r cos ****θ = f(θ) cos ****θ** , you get this:

**-2 = ***(θ + sin(2 θ)) cos ***θ **

Is this right? Am I just supposed to solve for*θ**?*

c) For π/3 < θ < 2π/3, dr/dθ is negative. What does this fact say about r? What does this fact say about the curve?

I am guessing that since dr/dθ is negative, 0>dr/dθ, which makes r decreasing. And because it is decreasing, the graph gets closer to the origin. Is this right?

d) Find the value of θ in the interval 0 ≤ θ ≤ π/2 that corresponds to the point on the curve in the first quadrant with greatest distance from the origin. Justify your answer.

**? I still don't know how to do this.**

I'd really appreciate any help you can offer. Thank you again!