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AP Calculus AB/BC
Unit 6 – Integration and Accumulation of Change
Topic 6.7
What is the second fundamental theorem of calculus?
If f(x) is continuous on an interval [a, b], then the integral of f(x) is equal to the derivative of F(x) evaluated at b
If f(x) is differentiable on an interval [a, b], then the integral of f'(x) is equal to F(x) evaluated at b minus F(x) evaluated at a
If f(x) is continuous on an interval [a, b], then the integral of f(x) is equal to F(b) - F(a), where F(x) is the antiderivative of f(x)
If f(x) is differentiable on an interval [a, b], then the integral of f'(x) is equal to f(b) - f(a)
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Second Fundamental Theorem of Calculus
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