AP Calculus AB, unit: Integration and Accumulation of Change. 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.
16 cards · basic cards · AI-written, checked twice. Edit anything.
- What is integration?
- The process of finding a function from its derivative, or of finding accumulated area under a curve
- What is an antiderivative?
- A function whose derivative is the given function
- What is the indefinite integral?
- The general antiderivative of a function, including an arbitrary constant of integration
- What does the constant of integration, C, represent?
- The fact that antiderivatives differ by a constant, since constants have a derivative of zero
- What is a definite integral?
- The signed area between a function's curve and the x-axis over a specific interval
- What is the Fundamental Theorem of Calculus?
- It connects differentiation and integration, showing they are inverse processes
- What does the first part of the Fundamental Theorem of Calculus state?
- The derivative of an accumulation function equals the original function evaluated at that point
- What does the second part of the Fundamental Theorem of Calculus state?
- A definite integral can be evaluated using any antiderivative of the function, evaluated at the bounds
- What is a Riemann sum?
- An approximation of a definite integral using the sum of areas of rectangles
- What is a left Riemann sum?
- A Riemann sum using the left endpoint of each subinterval to determine rectangle height
- What is a right Riemann sum?
- A Riemann sum using the right endpoint of each subinterval to determine rectangle height
- What is a midpoint Riemann sum?
- A Riemann sum using the midpoint of each subinterval to determine rectangle height
- What is the Power Rule for integration?
- The integral of x^n is x^(n+1) divided by (n+1), plus C, for n not equal to negative 1
- What is u-substitution used for?
- Simplifying an integral by substituting a portion of the integrand with a new variable
- What does accumulation of change mean, in the context of integrals?
- A definite integral represents the total change in a quantity over an interval
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