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Unveiling the Power Rule: Antiderivatives Discovery

Explore the process of finding antiderivatives, uncovering the power rule, and understanding the significance of constants in the general solution for indefinite integrals. Learn basic integration formulas and rules, and how to evaluate particular solutions effectively. Remember: don't forget dx or the constant 'C'! Discover the magic of antiderivatives today.

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Unveiling the Power Rule: Antiderivatives Discovery

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  1. Antiderivatives 5.1

  2. 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) =

  3. Differentiation Integration The process of finding a derivative The process of finding the antiderivative Tells us the variable of integration Symbols: Integral Symbols: Integrand

  4. 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!

  5. General Solution for an Indefinite Integral You will lose points if you forget dx or + C!!! Where c is a constant

  6. Basic Integration Formulas

  7. Find: You can always check your answer by differentiating!

  8. Basic Integration Rules

  9. Evaluate: C represents any constant

  10. Evaluate:

  11. Evaluate:

  12. Evaluate:

  13. Evaluate:

  14. Particular Solutions and F(1) = 0

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