Question

Calculate the area of the surface of revolution when the
function is revolved about the x-axis. Let ? = ?^2 (Q1) over the
interval 0 ≤ ? ≤ 3.

a) Setup the integral with respect to dx

b) Setup the integral with respect to dy

Answer #1

Compute the surface area of revolution about the x-axis over the
interval [0,π] for y=4sin(x)
(Use symbolic notation and fractions where needed.)

Find the surface area of revolution for y = 2
√x over (2,4), about the x-axis.

Find the area of the surface generated when the given curve
is revolved about the y-axis.
The part of the curve y= 1/2ln (2x + square root of
4x2 - 1 )between the pointe
(1/2,0) and (17/16,ln
2)

Find the surface area of the solid generated when the
region bounded by x=ln(2y+1),0≤y≤1 is revolved about the Y-
axis.

Find the exact area of the surface obtained by rotating the
curve about the x axis.
1. Original problem y= x^3 from 0 < x < 2
I got up to the SA= 2 pi the integral of 1 to 145 of (x^3)(the
square root of (1+9x^4))dx
I don't know how to integrate from this part on to get the exact
answer.

calculate the surface area of the solid x=sqrt9-y^2 from y=-2 to
y=2 which is revolved around the y axis
show full calculation

surface area of revolution y=(4-x^2/3)^3/2 about the xaxis over
[2,8].

The region bounded by ?=2+sin?, ?=0, ?=0 and 2? is revolved
about the ?y-axis. Find the volume that results.
Hint:
∫?sin???=sin?−?cos?+?
Volume of the solid of revolution:

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

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...

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