a) Sketch the curve defined by the equation r =
cos(20)
b) Sketch the region that lies inside the circle
r = 3 sin(0) and outside the cardioid r = 1+ sin/nc) Sketch the region: R= {(r, 0) : -/4 ≤ 0 ≤d) Sketch the region: R = {(r, 0) T ≤ 0 ≤
π/4,1 < r ≤ 2} and find its area.
3π/2,1 ≤ r ≤ 2} and find its area./ne) Sketch by hand the region:
R = {(x,y) : x ≤ y ≤ √√2-x²,0 ≤ x ≤ 1}.
f) Find the volume under the surface defined by
f(x, y) = y(x² + y²) ²
over the region R (see left) in the plane z = 0.
Convert this integral to polar coordinates and
evaluate it.
Fig: 1
Fig: 2
Fig: 3