Question

Region 2: Draw the region bounded by y=sqrt(x-2) and x-4y=2 .
Draw a representative rectangle

and label its base. Find the coordinates of and label all
intersection points. Then, find formulas for the

height of the rectangle .Also, set up an integral used to find the
area of the region. Evaluate the integral.

Answer #1

1. Find the Area of the region bounded by the graphs of
y=2x and y=x2-4x
a) Sketch the graphs, b) Identify the region, c) Find where the
curves intersect, d) Draw a representative rectangle, e) Set up the
integral, and f) Find the value of the integral.

The region is bounded by y=2−x^2 and y=x. (a) Sketch the region.
(b) Find the area of the region. (c) Use the method of cylindrical
shells to set up, but do not evaluate, an integral for the volume
of the solid obtained by rotating the region about the line x = −3.
(d) Use the disk or washer method to set up, but do not evaluate,
an integral for the volume of the solid obtained by rotating the
region about...

The region is bounded by y = 2 − x^ 2 and y = x
Use the method of cylindrical shells to set up, but do not
evaluate, an integral for the volume of the solid obtained by
rotating the region about the line x = −3

evaluate the double integral where f(x,y) = 6x^3*y - 4y^2 and D
is the region bounded by the curve y = -x^2 and the line x + y =
-2

Consider the plane region R bounded by the curve y = x − x 2 and
the x-axis. Set up, but do not evaluate, an integral to find the
volume of the solid generated by rotating R about the line x =
−1

Let R be the region of the plane bounded by y=lnx and the x-axis
from x=1 to x= e. Draw picture for each
a) Set up, but do not evaluate or simplify, the definite
integral(s) that computes the volume of the solid obtained by
rotating the region R about they-axis using the disk/washer
method.
b) Set up, but do not evaluate or simplify, the definite
integral(s) that computes the volume of the solid obtained by
rotating the region R about...

let R be the region bounded by the curves x = y^2 and x=2y-y^2.
sketch the region R and express the area R as an iterated integral.
(do not need to evaluate integral)

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.

Consider the region bounded by y=sqrt(x) and y=x^3
a) Find the area of this region
b) Find the volume of the solid generated by rotating this
region about the x-axis using washer
c) Find the volume of the solid generated by rotating this
region about the horizontal line y=3 using shells

Sketch the region enclosed by the given curves, decide whether
to integrate with respect to x or y. Draw a typical approximating
rectangle and label its height and width. Then find the volume of
the region rotated about the line y= -1. You do not need to full
solve the integral, just set it up properly
y = (X - 1)2, y = 1

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