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Calc 2 7.3

 

<== Calculus 2
Number Question Answer
See the work

1.

 

 

Find the volume of the solid obtained by rotating the
region bounded by
y=5sin(2x^2), 0≤x≤ sqrt(π/2
about the y axis

 

15.70796
The work

Point Cost: 3

2.

 

 

Use the method of cylindrical shells to find the
volume of the solid obtained by rotating the region
bounded by y= 7sqrt(x) and y= 7x^2 about the y axis.

 

1.885
The work

Point Cost: 4

3.

 

 

Use the method of cylindrical shells to find the volume
of the solid obtained by rotating the region bounded by
x= sqrt(y), x= 0 and y= 3, about the x axis.

 

39.178066
The work

Point Cost: 3

4.

 

 

 

 

The region bounded by y= x and y= 2x-x^2 is
rotated about the line x = 5.
Using cylindrical shells, set up an integral for the volume of
the resulting solid. The limits of integration are:
a=
b=
and the function to be integrated is:

 

a= 0
b= 1
ƒ(x)=2*π*(6*x-x^2-x)*(9-x)
The work

Point Cost: 1

5.

 

 

 

 

The region bounded by y= x^8 and y= sin(πx/2) is
rotated about the line x = -1.
Using cylindrical shells, set up an integral for the
volume of the resulting solid.
The limits of integration are:
a=
b=
and the function to be integrated is:

 

a= 0

b= 1

ƒ(x)= 2*π*(-x^8+sin(π*x/2))*(3+x)    

The work

Point Cost: 1

6.

 

 

 

 

The region bounded by y= 7/(1+x^2), y=0, x=0
and x= 2 is rotated about the line x=2.
Using cylindrical shells, set up an integral for the
volume of the resulting solid.
The limits of integration are:
a=
b=
and the function to be integrated is:

 

a= 0
b= 2
ƒ(x)=2π(5/(1+x^2))(3-x)
The work

Point Cost: 1

7.

Use the method of cylindrical shells to find the
volume generated by rotating the region bounded by
y=e^-x^2 y=0, x=0, and x=1 about the y-axis.

 

1.98587

The work

Point Cost: 3

8.

 

 

 

The region bounded by x^2-y^2=17, and x=9 is
rotated about the line y=10.
Using cylindrical shells, set up an integral for the
volume of the resulting solid.
The limits of integration are:
a=
b=
and the function to be integrated is:

a= -8

b= 8

ƒ(x)=2π(8-sqrt(17+y^2))(9-y)

The work

Point Cost: 2