Reverse a known derivative
Differentiating x³ gives 3x². Finding an antiderivative asks for a function whose derivative is the given integrand.
Calculus / English
Integrals AKA Antiderivatives EXPLAINED with Examples
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Understand indefinite integration as finding a family of antiderivatives rather than one original function.
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0:19Reverse a known derivative1:34Constants disappear on differentiation3:24Check the whole familyLearning script
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Differentiating x³ gives 3x². Finding an antiderivative asks for a function whose derivative is the given integrand.
The functions x³, x³+2 and x³+100 share the same derivative. An indefinite integral therefore includes an arbitrary constant C.
The antiderivative family of 3x² on a connected interval is x³+C. Differentiating any member verifies the answer; a definite integral additionally uses specified bounds.
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Constants disappear on differentiation
The functions x³, x³+2 and x³+100 share the same derivative. An indefinite integral therefore includes an arbitrary constant C.
Check the whole family
The antiderivative family of 3x² on a connected interval is x³+C. Differentiating any member verifies the answer; a definite integral additionally uses specified bounds.
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- Antiderivatives ExplanationAt 0:19
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Differentiating x³ gives 3x². Finding an antiderivative asks for a function whose derivative is the given integrand. The functions x³, x³+2 and x³+100 share the same derivative. An indefinite integral therefore includes an arbitrary constant C. The antiderivative family of 3x² on a connected interval is x³+C. Differentiating any member verifies the answer; a definite integral additionally uses specified bounds.
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