Question

Find the exact length of the curve.

Part A

x = 4 + 12t^{2}, y = 7 + 8t^{3} , 0 ≤ t ≤ 1

Find the exact length of the curve.

Part B

x = e^{t} - 9t, y = 12e^{t/2} , 0 ≤ t ≤ 2

Answer #1

Find the exact length of the curve.
x = 4 +
12t2, y
= 1 + 8t3, 0 ≤
t ≤ 3
please give answer with radicals. cannot have decimals.

Find the exact length of the curve.
x = 9 +
12t2, y
= 2 + 8t3, 0 ≤
t ≤ 5

Find the exact length of the curve.
x = 5 +
12t2, y
= 8 + 8t3, 0 ≤
t ≤ 5

Find the exact length of the curve. x = 8 + 9t2, y = 3 + 6t3, 0
≤ t ≤ 5
Find an equation of the tangent to the curve at the given point
by both eliminating the parameter and without eliminating the
parameter. x = 6 + ln(t), y = t2 + 1, (6, 2) y =
Find dy/dx. x = t 3 + t , y = 3 + t
Find the distance traveled by a particle...

Find the exact length of the curve.
y2 = 4(x + 3)3, 0 ≤ x ≤
1, y > 0

Find the exact length of the curve y=(x^3)/3 + 1/(4x) for
2≤x≤3
Conslder the curve deflned by x=t+1 and y=t^2. Find the
corresponding rectangular equation. Produce two graphs: one using
the rectangular equation and one using the parametric equations.
What are the differnce's between the graphs?
Please show work.

Find the exact length of the curve.
y = ln(sec x), 0 ≤
x ≤ π/3

Find the length of the curve defined by the parametric
equations
x=(3/4)t y=3ln((t/4)2−1)
from t=5 to t=7.

Find the exact area of the surface obtained by rotating the
curve about the x-axis.
A. y = sqrt(1+ex ) , 0 ≤ x ≤ 3
B. x = 1/3(y2+2)3/2 , 4 ≤ x ≤ 5

Find the length of the curve
1) x=2sin t+2t, y=2cos t, 0≤t≤pi
2) x=6 cos t, y=6 sin t, 0≤t≤pi
3) x=7sin t- 7t cos t, y=7cos t+ 7 t sin t, 0≤t≤pi/4

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