Test practice: Antiderivatives, Area, & FTC

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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 u-substitution in integration?

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U-substitution is a method used to simplify the integration process by substituting a part of the integrand with a new variable u, making the integral easier to solve.

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What is the Fundamental Theorem of Calculus?

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How do you find the area under a curve using definite integrals?

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What does the constant 'c' represent in antiderivatives?

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The constant 'c' represents the arbitrary constant of integration, which accounts for all possible antiderivatives of a function.

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How do you evaluate a definite integral graphically?

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To evaluate a definite integral graphically, find the area between the curve and the x-axis over the specified interval, considering areas above the x-axis as positive and below as negative.

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What is the significance of fractional exponents in integration?

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Fractional exponents allow for the representation of roots in a more manageable form, making integration easier, especially in polynomial and rational functions.

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