Question

1. Find the Area of the region bounded by the graphs of
*y=2x* and *y=**x**2**-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.

Answer #1

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.

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...

Find the area of the region bounded by the graphs:
y=x^2-4
y=x^4-4x^2
I set the equations equal to one another then solved for zero,
but I am stuck after getting x^4-5x^2+4

1) Find the area of the region bounded by the curves y = 2x^2 −
8x + 12 and y = −2x + 12
a) Find the volume when the area in question 1 is revolved
around the x-axis.
b)Find the volume when the area in question 1 revolved around
the y-axis.

Find the area of the region bounded by the graphs of the given
equations.
y=2x^2-9x+13, y=x^2+3x-7

Find the area of the region bounded between the functions f(x)=
x2 – 2x + 2 and g(x) = -x2 + 6.

Find the area of the region enclosed by the curves
y=x2+2x, y=x2-6x+8 and the line y= -1.

Given that D is a region bounded by x = 0, y = 2x, and y =
2.
Given:
∫
∫
x y dA , where D is the region bounded by x = 0, y = 2x, and y =
2.
D
Set up iterated integrals (2 sets) for both orders of
integration. Need not evaluate the
Integrals. Hint: Draw a graph of the region D. Consider D as a
Type 1 or Type 2 region.
Extra credit problem

Find the area of the region between the graphs of f(x) = 3x3 −
x2 − 10x and g(x) = −x2 + 2x.

Sketch the region enclosed by the curves and find its area.
y=x,y=4x,y=−x+2
AREA =

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