AP Calculus BC: 9.8 Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve – Exam Style questions with Answer- FRQ

Question

 Consider the curve defined parametrically by  \(x=\sin t-\cos t\) and \(y=\sin t+\cos t\)
(A) Find the length of the curve from \(\frac{\pi }{4}\leq t\leq \frac{\pi }{2}\) .
(B) Find the area bounded underneath the curve from \(\frac{\pi }{4}\leq t\leq \frac{\pi }{2}\)
(C) Find the area of the surface generated by revolving about the x-axis the parametric curve defined from \(\frac{\pi }{4}\leq t\leq \frac{\pi }{2}