Question

1. Find the area of the region enclosed between y=4sin(x) and y=4cos(x) from x=0 to x=0.5π

2. Find the volume of the solid formed by rotating the region enclosed by

x=0, x=1, y=0, y=8+x^5

about the x-axis.

3. Find the volume of the solid obtained by rotating the region bounded by

y=x^2, y=1.

about the line y=7.

Answer #1

Find the volume V of the solid obtained by rotating the
region bounded by the given curves about the specified line.
y = 5x4, y = 5x, x ≥
0; about the x-axis
Find the area of the region enclosed by the given curves.
y = 3 cos(πx), y = 12x2 −
3
Find the volume V of the solid obtained by rotating the
region bounded by the given curves about the specified line.
2x = y2, x = 0, y =
5; about the...

Find the volume of the solid formed by rotating the region
enclosed by
x=0,x=1,y=0,y=4+x^6
about the y-axis.
Volume =

Find the area of the region enclosed between y=4sin(x) and
y=4cos(x) from x=0 to x=0.4π. Hint: Notice that this region
consists of two parts.

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

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...

1) Find the volume of the solid formed by rotating the region
enclosed by
y=e^(5x)+2, y=0, x=0, x=0.4
about the x-axis.
2) Use the Method of Midpoint Rectangles (do NOT use the
integral or antiderivative) to approximate the area under the curve
f(x)=x^2+3x+4 from x=5 to x=15. Use n=5 rectangles to find your
approximation.

Find the volume of the solid formed by rotating the region
enclosed by
y=e^2x +5 , y=0, x=0, x=1, about the x axis.

there are 5 parts to this question
1.Find the area of the region R enclosed by the graphs of y = x
2 , the y-axis and the line y = 4
2.Find the volume of the solid generated by revolving the region
in problem 1 about the x-axis.
3.Use the cylindrical shell method to find the volume of the
solid generated by revolving the region in problem 1 about the
y-axis.
4.Find the volume of the solid generated by...

1) Find the volume of the solid obtained by rotating the region
enclosed by the graphs about the given axis. ?=2?^(1/2), y=x about
y=6 (Use symbolic notation and fractions where needed.)
2) Find the volume of a solid obtained by rotating the region
enclosed by the graphs of ?=?^(−?), y=1−e^(−x), and x=0 about
y=4.5.
(Use symbolic notation and fractions where needed.)

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.

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