AP Calculus AB, unit: Applications of Integration. Conceptual understanding and key rules for this unit, explained in plain language alongside the formula. Front: a concept or short problem cue. Back: the explanation, rule, or answer.
12 cards · basic cards · AI-written, checked twice. Edit anything.
- What does a definite integral represent geometrically?
- The signed area between a curve and the x-axis over an interval
- How is the area between two curves calculated?
- Integrating the difference between the upper and lower functions over the interval
- What is the disk method used for?
- Finding the volume of a solid of revolution by integrating circular cross-sectional areas
- What is the washer method used for?
- Finding the volume of a solid of revolution with a hole, using the difference of two disk areas
- What is the shell method used for?
- Finding the volume of a solid of revolution by integrating cylindrical shell surface areas
- What is average value of a function over an interval?
- The definite integral of the function over the interval, divided by the interval's length
- How is total displacement found from a velocity function?
- Taking the definite integral of the velocity function over the time interval
- How is total distance traveled found from a velocity function?
- Integrating the absolute value of the velocity function over the time interval
- What is net change, as found using integration?
- The definite integral of a rate of change function, representing total accumulated change
- What is arc length, in single-variable calculus, computed using?
- An integral involving the square root of one plus the derivative squared
- How do you set up an integral to find the volume of a solid with known cross-sections?
- Integrating the area of each cross-section along the axis of the solid
- What is the significance of the sign of a definite integral?
- A positive value indicates area above the x-axis; a negative value indicates area below it
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