Question

Question(9) Curve ? = t - sin t, y = 1 - cos t, 0 ≤ ? ≤ 2? given.

a) Take the derivatives of x and y according to t and arrange them.

b) Write and edit the integral that gives the surface area of the object formed by rotating the given curve around the x axis.

c) Solve the integral and find the surface area.

Answer #1

Consider the parametric equations below.
x = t sin(t), y = t
cos(t), 0 ≤ t ≤ π/3
Set up an integral that represents the area of the surface
obtained by rotating the given curve about the x-axis.
Use your calculator to find the surface area correct to four
decimal places

8?^2 = ?^2 (1 − ?^2) gives on x plane
?please take this function's derivative and orginized
?) Write and edit the integral that sees the surface area of
the object formed by turning the given part around the
x-axis.
?)solve the integral and find the surface area

The curve given by the parametric equations of x = 1-sint, y = 1-cos t ,
Calculate the volume of the rotational object formed by rotating the x axis use of the parts between t = 0 and t = π / 2.
Please solve this question carefully , clear and step by step.I
will give you a feedback and thumb up if it is correct.

With the parametric equation x=cos(t)+tsin(t), y=sin(t)-tcos(t)
, 0 ≤ t ≤ 2π)
Find the length of the given curve. (10 point)
2) In the circle of r = 6, the area
above the r = 3 cos (θ) line
Write the integral or integrals expressing the area of this
region by drawing. (10 point)

2. Rotate the semicircle of radius 2 given by y = √(4 − x^2)
about the x-axis to generate a sphere of radius 2, and use this to
calculate the surface area of the sphere.
3. Consider the curve given by parametric equations x = 2
sin(t), y = 2 cos(t).
a. Find dy/dx
b. Find the arclength of the curve for 0 ≤ θ ≤ 2π.
4.
a. Sketch one loop of the curve r = sin(2θ) and find...

1. Find the area between the curve f(x)=sin^3(x)cos^2(x) and y=0
from 0 ≤ x ≤ π
2. Find the surface area of the function f(x)=x^3/6 + 1/2x from
1≤ x ≤ 2 when rotated about the x-axis.

Show that the curve
x = 7 cos(t), y = 6 sin(t) cos(t)
has two tangents at (0, 0) and find their equations.

Calculate the volume of the rotational object formed by rotating
the given curve with the parametric equations x = 1-sint, y = 1-cos
t about the x-axis between the part between t = 0 and t = π /
2.

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

Fidn the area of the surface of the rotating curve y=(10-x)^1/2
from 0<y<5 about the x-axis. olease write neat .

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