Antiderivatives, Riemann Sums & Definite Integrals

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What is an antiderivative?

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An antiderivative of a function f(x) is a function F(x) such that F'(x) = f(x). It represents the reverse process of differentiation.

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What is the Fundamental Theorem of Calculus?

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What is a Riemann Sum?

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A Riemann Sum is a method for approximating the total area under a curve by dividing it into intervals and summing the areas of rectangles formed.

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What are the types of Riemann Sums?

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The types of Riemann Sums include Left Riemann Sum, Right Riemann Sum, and Midpoint Riemann Sum, depending on how the heights of the rectangles are determined.

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What is the formula for the area under a curve using Riemann Sums?

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What is the significance of the constant C in antiderivatives?

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The constant C represents the family of all antiderivatives, as the derivative of a constant is zero.

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What is a definite integral?

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How do you approximate the area under a curve using 4 intervals with left values?

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To approximate, calculate the height of the function at the left endpoint of each interval and sum the areas of the rectangles formed.