Calculus
Applications of integration
- Finding the average value of a function on an interval
- Connecting position, velocity, and acceleration functions using integrals
- Using accumulation functions and definite integrals in applied contexts
- Finding the area between curves expressed as functions of x
- Finding the area between curves expressed as functions of y
- Finding the area between curves that intersect at more than two points
- Volumes with cross sections: squares and rectangles
- Volumes with cross sections: triangles and semicircles
- Volume with disc method: revolving around x- or y-axis
- Volume with disc method: revolving around other axes
- Volume with washer method: revolving around x- or y-axis
- Volume with washer method: revolving around other axes
- The arc length of a smooth, planar curve and distance traveled
- Calculator-active practice
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Calculus · series session
Applications of integration
Integral Applications: Accumulation
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kishan p
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1/5
Ai
Calculus · series session
Applications of integration
Integral Applications
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kishan p
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1/5
Ai
Calculus · series session
Applications of integration
Unit 8 of the AP Calculus BC Course.
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Sahasra J
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21/30
Ai
Calculus · series session
Applications of integration
We will solve problems from Unit 8 of the AP Calculus BC course.
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Sahasra J
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21/30
Ai
Calculus · series session
Applications of integration
Areas and volumes with integrals!
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Luca G
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Ai
Calculus · series session
Applications of integration
1. Physical interpretations of the integral and the average value of a function over an interval
2. Finding the area between curves expressed as functions of y
3. Finding the area between curves that intersect at more than two points
4. Volumes with cross sections: squares, rectangles, (part 1)
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Jose Roberto Cossich G
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6/10
Ai
Calculus · series session
Applications of integration
6. (part 2) triangles, and semicircles
5. Volume with the disc and washer method: revolving around x-, y-, and different axes
6. Arc length, distance traveled, and unit calculator practice
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JG
Jose Roberto Cossich G
0
6/10
Ai
Calculus · series session
Applications of integration
Unit I Test (1h 20m) - Khan Academy -
AP Calc BC
"Unit 6: Integration and accumulation of change"
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Jose Roberto Cossich G
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6/10
Ai
Calculus · series session
Applications of integration
8.1 - How can you find the average value for a function across an interval?
8.2 - Can you apply integrals in a physics context?
8.3 - Can you apply the FTC(definite integrals) in various contexts?
8.4, 8.5, 8.6 - Can you find the area between two or more curves, whether they’re functions of x or y?
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William B
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Ai
Calculus · series session
Applications of integration
8.7 and 8.8 - Can you find the volume of solids with a cross section representing squares, rectangles, triangles, or semicircles?
8.9 and 8.10 - Can you find the volume of a solid with a rotating cross section using the disc method?
8.11 and 8.12 - Can you find the volume of a solid with a rotating cross section using the washer method?
(BC only) 8.13 - Can you find the arc length of a function?
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WB
William B
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7/50
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