Question

Set up an integral

that gives an average value x³ sin x

interval [-2, 1].

Answer #1

Set up a double integral in rectangular coordinates for the
volume bounded by the cylinders x^2+y^2=1 and y^2+z^x=1 and
evaluate that double integral to find the volume.

when cylinder x^2+y^2=1, y^2+z^1=1 and x^2+z^1=1 intercept with
each other, set up a triple integral to calculate the volume of the
interception. (Dont have to evaluate the integral, but just set it
up.)

Set up the triple integral, including limits, of the function
over the region.
f(x, y, z) = sin z, x ≥ 0, y ≥ 0, and below the plane 2x + 2y +
z = 2

Please answer all question explain. thank you.
(1)Consider the region bounded by y= 5- x^2 and y = 1. (a)
Compute the volume of the solid obtained by rotating this region
about the x-axis.
(b) Set up the integral for the volume of the solid obtained by
rotating this region about the line x = −3. No need to evaluate the
integral, just set it up.
(2) (a) Find the exact (no calculator approximation) average
value of the function f(x)...

Let S be the region between •x=1, •x=3, •y=6−(x−2)2, and •y=x
2+1.
a) Set up an integral to ﬁnd the area of S. Do not
evaluate.
b) Set up an integral to ﬁnd the volume Vx of the solid obtained by
rotating S about the x-axis. Do not evaluate.
c) Set up an integral to ﬁnd the volume Vy of the solid obtained by
rotating S about the y-axis. Do not evaluate.

Consider the integral ∫∫R(x^2+sin(y))dA where R is the region
bounded by the curves x=y^2, x=4, and y=0. Setup up this
integral.

Set up, but do not solve, the triple integral for determining
the mass of the sphere ? = 10 sin? sin ? with a density of ?(?,?,
?) = ?.

6.(8pts) Find the Average value of ?(?) = 5? sin(?2)
on the interval [ 0, √? ]

1. The graph of y = f(x) = 1/ x^2 , 1 ≤ x < ∞, is rotated
around the x-axis.
(a) Calculate the resulting volume.
(b) Set up the integral that gives the resulting surface area,
but DO NOT WORK OUT THE INTEGRAL.

A>Set up an integral that calculates the volume of the solid
described below using the washer method. Do not
evaluate the integral. f(x) = (x − 1)^2 − 1, x = −1, x = 1, y = 3,
about x = −3
B>Set up another integral that calculates the volume of the
solid from A using the shell method. Again, do not
evaluate the integral.
Include sketches for the following A AND B
Please write down the detailed process, thank...

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