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Antiderivatives 5.1
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Discovery of Power Rule for Antiderivatives
If f ‘ (x) = Then f(x) = If f ‘ (x) = Then f(x) = If f ‘ (x) = Then f(x) = If f ‘ (x) = Then f(x) =
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Tells us the variable of integration
Differentiation Integration The process of finding a derivative The process of finding the antiderivative Tells us the variable of integration Symbols: Integral Symbols: Integrand
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The antiderivatives vary by a constant!
is the indefinite integral of f(x) with respect to x. Each function has more than one antiderivative (actually infinitely many) Derivative of: The antiderivatives vary by a constant!
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General Solution for an Indefinite Integral
You will lose points if you forget dx or + C!!! Where c is a constant
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Basic Integration Formulas
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You can always check your answer by differentiating!
Find: You can always check your answer by differentiating!
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Basic Integration Rules
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C represents any constant
Evaluate: C represents any constant
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Evaluate:
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Evaluate:
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Evaluate:
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Evaluate:
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Particular Solutions and F(1) = 0
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