Calculus 2: Applications of Integrals
36 videos • 8,792 views • by Math Problems Solved Craig Faulhaber
1
Derive the formula for the volume of a sphere using the volume by slicing method
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2
Derive the formula for the volume of a cone using the slicing method
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3
Find the volume of liquid needed to fill a sphere of radius R to a height of R/4
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4
Use calculus to find the volume of the solid S with the given base and square cross sections
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5
Use Calculus to find the volume of the cap of a sphere with height h and radius r.
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6
Draw the region bounded by the curves y=e^x+1, x=0, x=1, y=0 and use the disk method to find the ...
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7
Use the disk method to find the volume of the region bounded by y=sqrt(x), x=4, y=0, rotated about..
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8
Rotate the region bounded by the curves y=sqrt(4-x^2), x=0, y=0 about the y-axis. Find the volume...
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9
We have a region bounded by y=1/(x+1), x=0, x=2. Use the disk method to find the volume created...
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10
Use the washer method to find the volume of the region y=x+2, y=x+6, x=0, x=5 rotated about...
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11
The region bounded by y^3=x^2 and y^2=x^3 is rotated about the x-axis. Find the volume using washers
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12
Draw the region bounded by the curves y=sqrt(x), x=4, y=0. Use the washer method to find the volume
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13
Find the volume of the region between y=2x and y=x^2 when rotated about y=4 using the washer method
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14
Find the volume of the solid obtained by rotating the region bounded by x=y^4, x=1 about x=2
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15
Find the volume using shells. The region bounded by y=1/x^5, y=0, x=1, x=5 rotated about the y-axis
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16
Use shells to find the volume of the region between y=x^3, y=8, x=0, rotated around the x-axis
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17
Find the volume of the solid formed by rotating the region bounded by y=x^2, x=2, x=3, y=0 about x=5
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18
Use the method of cylindrical shells to find the volume generated by rotating the region bounded...
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19
Find the arc length of y=x^(2/3) over the interval from (1,1) to (8,4)
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20
Find the length of the arc formed by x^2=7y^3 from A=(0,0) to B=(49,7)
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21
Find the arc length of y=x^3/6 +1/2x from x=1/2 to x=1
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22
Find the arc length of y=x^3/6 +1/2x from x=1/2 to x=1
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23
Find the arc length of y=int_1^x sqrt(t^3-1) dt from x=1 to x=4
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24
Find the length of the curve y=ln(secx) from x=0 to x=pi/4
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25
Find the surface area of the volume generated by rotating y=3x^3 about the x-axis from x=0 to x=3
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26
Find the surface area of revolution generated by rotating y=x^(1/3) about the y-axis from y=1 to y=4
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27
A group of engineers is building a parabolic satellite dish whose shape will be formed by rotating..
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28
Compute the surface area of revolution of y=sinx about the x-axis over the interval [0,7pi]
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29
Compute the work done by a force of F(x)=12/x^2 from x=1 to x=2
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30
A cylinder of depth H and cross sectional area A stands full of water at density rho. Find the work
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31
A tank in the shape of a cylinder is filled with hot chocolate. Find the work needed to empty the...
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32
Compute the mass of the 2 ft long wire (starting at x=0) with the density of rho(x)=x^2+2x lb/ft
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33
Compute the center of mass given rho(x)=cosx on the interval [0,pi/2]
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34
Compute the center of mass given rho=sqrt(x) on the interval [1,4]
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35
Compute the center of mass of the triangle with vertices (0,0), (a,0), (0,b) given a constant...
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36
Find the centroid of the region lying between y=7sinx and y=7cosx over the interval [0,pi/4]
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