Question

Find the arc length (exact value) of the polar curve r = 2sintheta
+ 4 costheta.

0 <= theta <= 3pi/4 by setting up and evaluating a
definite integral.

Answer #1

Find the length of the polar curve r = e^-theta, o lesser or
equal to theta lesser or equal to 3pi. Please write as large and
neatly as possible. Thank you.

a) Set up the integral used to find the area contained in one
petal of r= 3cos(5theta)
b) Determine the exact length of the arc r= theta^2 on the
interval theta= 0 to theta=2pi
c) Determine the area contained inside the lemniscate r^2=
sin(2theta)
d) Determine the slope of the tangent line to the curve r= theta
at theta= pi/3

Find the arc length of the curve r(t) = i + 3t2j +
t3k on the interval [0,√45].
Hint: Use u-substitution to integrate.

Find, for 0 ≤ x ≤ π, the arc-length of
the segment of the curve R(t) = ( 2cost − cos2t, 2sint −
sin2t )
corresponding to 0 ≤ t ≤ x.

3)
a) Find a polar equation for the circle x^2 + (y -2)^2 = 4.
b)Find the arc length of the polar curve r =
3^θ from θ=0 to θ=2.

Find the Arc Length of the cardioid r = 1 + sin(theta), using
the substitution method u = tan(theta/2)

Find the exact length of the curve.
Part A
x = 4 + 12t2, y = 7 + 8t3 , 0 ≤ t ≤ 1
Find the exact length of the curve.
Part B
x = et - 9t, y = 12et/2 , 0 ≤ t ≤ 2

Given the polar curve: r = cos(theta) - sin(theta)
Find dy/dx

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

Find the exact length of the curve. 36y2 = (x2 − 4)3, 4 ≤ x ≤ 6,
y ≥ 0

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