Question

3. Set up two double integrals giving the area enclosed by the curves y = x^2 and y = x + 2 and evaluate one of them.

Answer #1

Evaluate the following integrals:
a.) Find the area enclosed by y = (ln(x))/ (x^2) and y =
(ln(x))^2/x2 ;
b.) Find the volume of the solid formed by revolving the region
under y = e^ 3x for 0 ≤ x ≤ 3 about the y -axis.

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

Set up iterated integrals for both orders of integration. Then
evaluate the double integral using the easier order.
y dA, D is bounded by y = x
− 20; x = y2
D

Find the area of the region enclosed by the curves x=2y and
4x=y^2

Sketch the region enclosed by the given curves and find its
area:
a)y=x^2-4
b)y=x+2 1<=x<=4

Graph y = x3 and y = x on [0, 2].
1) graph of the area between the curves y = x3 and y
= x on [0, 2] includes _____________
distinct areas.
2) One of my shaded areas has area =
3) One of my shaded areas has area =
4)
The graph showing the area between the two curves y =
x3 and y = x has four intersection points. Which of the
following points is not an intersection...

Sketch the region enclosed by the curves y=x(1-x) and y=-9x+9
then compute its area.

1.Find the area of the region between the curves y= x(1-x) and y
=2 from x=0 and x=1.
2.Find the area of the region enclosed by the curves
y=x2 - 6 and y=3 between their
interaction.
3.Find the area of the region bounded by the curves
y=x3 and y=x2 between their interaction.
4. Find the area of the region bounded by y= 3/x2 ,
y= 3/8x, and y=3x, for x greater than or equals≥0.

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.

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.

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