A polar curve is defined by the equation r=θ+sin2θ for 0≤θ≤pi.
a) Find the area bounded by the curve and the x-axis.
b) Find the angle θ that corresponds to the point on the curve where x=-2.
c) For pi/3<θ<2pi/3, dr/dθ is negative. How can this be seen from the graph?
d) At what angle θ in the interval 0≤θ≤pi/2 is the curve farthest away from the origin? Justify your answer.
Please show complete work. Thanks.