Question

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.

Answer #1

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

a)Find the length of half cardioid r = 2-2costheta
b)Find the area of the region that is within r = a (1+ cos
theta) and outside r = a (cos theta)

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 inside of r=1+cos theta, but outside of r=1+sin
theta

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.

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

1.
Find the arclength of r=cos^(3)(theta/3)
2. Find the area outside r=3 and inside
r^2=18cos(2•theta)
3. Find the slope of the tangent line to r=2sin(4•theta) at
theta=pi/4

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

2. (a) Find the point on the cardioid r = 2(1 + sin θ) that is
farthest on the right.
(b) What is the area of the region that is inside of this
cardioid and outside the circle r = 6 sin θ?

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