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.
37 cards · basic cards · AI-written, checked twice. Edit anything.
- What does a definite integral represent geometrically?
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The signed area between a curve and the x-axis over an interval- How is the area between two curves calculated?
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Integrating the difference between the upper and lower functions over the interval- What is the disk method used for?
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Finding the volume of a solid of revolution by integrating circular cross-sectional areas- What is the washer method used for?
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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?
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Finding the volume of a solid of revolution by integrating cylindrical shell surface areas- What is average value of a function over an interval?
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The definite integral of the function over the interval, divided by the interval's length- How is total displacement found from a velocity function?
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Taking the definite integral of the velocity function over the time interval- How is total distance traveled found from a velocity function?
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Integrating the absolute value of the velocity function over the time interval- What is net change, as found using integration?
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The definite integral of a rate of change function, representing total accumulated change- What is arc length, in single-variable calculus, computed using?
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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?
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Integrating the area of each cross-section along the axis of the solid- What is the significance of the sign of a definite integral?
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A positive value indicates area above the x-axis; a negative value indicates area below it- What is the formula for the disk method when revolving a region around the x-axis?
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V = pi times the integral from a to b of [f(x)]^2 dx- What is the formula for the disk method when revolving a region around the y-axis?
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V = pi times the integral from c to d of [g(y)]^2 dy, integrating with respect to y- What is the formula for the washer method?
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V = pi times the integral from a to b of ([R(x)]^2 minus [r(x)]^2) dx, where R is the outer radius and r is the inner radius
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