Question

Determine the surface area of a funnel that is generated by revolving the graph of y = f(x) = x^3 + (1/12x) on the interval from [1, 2] about the x-axis.

Answer #1

Find the area of the surface generated by revolving the curve x
= ?square root 4y − y2, 1 ≤ y ≤ 2, about y-axis.

Find the area of the surface of revolution that is generated by
revolving the curve x= (y^4)/8 + (y^-2)/4, from y=2 to y=5, about
the line x=-1

Compute the surface area of the surface generated by revolving
the curve ?(?)=(?,??)c(t)=(t,et) about the ?-x-axis for 0≤?≤1.

Section 2 Problem 4:
a)Find the area of the surface obtained by rotating the
curvex=1/3((y^2)+2)^(3/2), 1<=y<=2, about the x-axis
b)Find the area of the surface generated by revolving the given
curve about the y-axis. x=sqrt(25-y^2), -4<=y<=4

Find the volume generated by revolving about the x-axis the
region bounded by the following graph.
y=sqrt(2x+3), x=0, x=1

Find the volume of the solid generated by revolving
the area bounded by the given
curves/lines about the indicated axis using both vertical and
horizontal elements if applicable.
y=x² ,x=1, y=0
a. about the axis
b. about x=1
c. about the y-axis

1) Find the arc length of the graph of the
function over the indicated interval. Show your work.
y=ln(cosx) ; [ 0 ,
π/4]
2)
Find the surface area generated by revolving
the graph about the x - axis over the indicated interval. Show your
work.
y=2x ; [ 0 , 3
]

Find the volume of the solid generated by revolving the region
bounded by y = sqrt(x) and the lines and about y=2 and x=0
about:
1) the x-axis.
2) the y-axis.
3) the line y=2.
4) the line x=4.

Consider the curve y = e sin x for π /6 ≤ x ≤ π /3 . Set up the
integrals (without evaluating) that represent
1. The area of the surface generated by revolving the curve
about the x-axis.
2. The area of the surface generated by revolving the curve
about the y-axis.

Find the volume of the solid generated by revolving the region
bounded by y = 2ex - 4x, y = 2 - 2x, x = 0, x = 1 about
the x-axis using the most appropriate method.

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