Question

Consider the polar curve ? = cos(?) + 1. To find the area enclosed by the curve, a student computes: A = ∫ 1/2(???2? + 2???? + 1)??. bounds (0,pi) Explain the mistake.

Answer #1

1.Find the area of the region specified in polar
coordinates.
One leaf of the rose curve r = 8 cos 3θ
2.Find the area of the region specified in polar
coordinates.
The region enclosed by the curve r = 5 cos 3θ

[Find the area of a region bounded by a polar curve.]
Find the area enclosed by the inner loop of r=3
−6cosθ. Round the answer to three decimal places.

Find the area that lies simultaneously outside the polar curve r
= cos θ and inside the polar curve r = 1 + cos θ.

Sketch the curve.
r = 4 + 2 cos(θ) and find area enclosed by it.

given the polar curve r = 2(1+cos theta) find the Cartesian
coordinates (x,y) of the point of the curve when theta = pi/2 and
find the slope of the tangent line to this polar curve at theta =
pi/2

1, Find the area enclosed by the lemniscate of bernoulli r^2 =
9cos (2theta)
2. find the area enclosed between the parabola r = 1/1 +
cos(theta) and the line cos theta = 0
3. find the area enclosed in the second and third quadrants by
the curve x = t^2 - 1 , y = 5t^3(t^2 - 1)
4. find the area of enclosed by the curve y^2 = x^2 - x^4
5. find the area loop of the...

Find the area of the region soecified. The region enclosed by
the curve r= 5 +cos(theta)

Consider the polar curve r =1 + 2 cos(theta). Find dy dx at
theta = 3 .

Consider the polar curve r = 2 cos theta. Determine the slope of
the tangent line at theta = pi/4.

Find the area enclosed by the function r = 1 – cos θ

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