Calculus 1: Areas and Volumes using Integrals
34 videos • 2,312 views • by Math Problems Solved Craig Faulhaber
1
Write an integral to represent the area between the curves y=x^2-1 and y=6
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2
Set up and solve an integral to represent the area between the curves y=x^2 and y= 6x + 7
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3
Use two integrals to find the area between the curves y=cosx and y=1/2 on the interval [0,3pi/2]
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4
Find the area of the region bounded by the graphs y=e^4x, y=e^-5x, x=-1, x=2
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5
Find the area of the region bounded by the graphs y=x^3 and y=5x
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6
Find the value of c that makes the area between the parabolae y=x^2-c^2 and y=c^2-x^2 equal to 576
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7
Find the area of the shaded region below between the functions x=y^2-4y and x=2y-y^2
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8
Derive the formula for the volume of a sphere using the volume by slicing method
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9
Derive the formula for the volume of a cone using the slicing method
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10
Find the volume of liquid needed to fill a sphere of radius R to a height of R/4
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11
Use calculus to find the volume of the solid S with the given base and square cross sections
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12
Use Calculus to find the volume of the cap of a sphere with height h and radius r.
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13
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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14
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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15
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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16
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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17
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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18
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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19
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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20
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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21
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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22
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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23
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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24
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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25
Use the method of cylindrical shells to find the volume generated by rotating the region bounded...
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26
Calculus POD #63 displacement vs distance
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27
Calculus POD 64 Find the position and velocity of an object with the given acceleration, initial...
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28
Calculus POD 65 Find the area of the shaded region shown in the graph
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29
Calculus POD 66 Find the area of the shaded region shown in the figure between y=7-x and x=(y-4)^2/4
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30
Calculus POD 67 Find the area of the shaded region between cosx and cos2x
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31
Calc POD 68 Disk Method. Find the volume of the solid generated by revolving the region bounded by..
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32
Calc POD 69 Washer Method: Find the volume of the solid generated when R is revolved about the x-axi
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33
Calculus POD 70 Shell Method. Find the volume of the solid generated when R is revolved about the y
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34
Calculus POD 71 Use both the Shell and Disk/Washer Methods to find the volume of revolution
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