Question

What is the area of the region common to two regions bounded by circle r=3, and a cardioid r=3(1+sinθ)?

Answer #1

Find the area of the region inside the circle r = sqrt(3) sinx
and outside cardioid r = 1 + cosx

determine
the value of a for which the area of the region bounded by the
cardioid r=a(1-cosΘ) is equal to 9π square units; The arc length of
the cardioid

Find the area of the region inside the circle r = sin θ but
outside the cardioid r = 1 – cos θ. Hint, use an identity for cos
2θ.

Find the area of the region that is outside the cardioid r = 1
+cos (theta) and inside the circle r = 3 cos (theta), by
integration in polar coordinates.

2. Find the area of the region that lies inside the curve r=3
sinθ and outside of the curve r= 1+sinθ

Find the exact area of the region inside the circle
r=2cos(theta) but outside the circle r=1

a) Sketch the graph of r = 1 + sin2θ in polar coordinates with
proper explanation.
b) Find the area of the region that is inside of the cardioid r
= 2+2sinθ and outside of the circle r = 3. Also ﬁnd the area that
is outside of the cardioid and inside of the circle. Hence, ﬁnd the
total area enclosed by these two curves.

Use a double integral to find the area inside the circle
r = cos θ and outside the cardioid r = 1 − cos θ.

Find the area of the region within the cardioid r = 1 − cos θ
for θ ∈ [0, π /2]

Find area of the region inside of the rose, r=6sin2θ and inside
the circle r =3sqrt(2)

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