Indefinite Integrals - 13.1 Indefinite Integrals The Indefinite Integral or antiderivative of a function is the function such that â€² = Notation ï¿½

# Indefinite Integrals - 13.1 Indefinite Integrals The...

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13.1 Indefinite Integrals The Indefinite Integral, or antiderivative, of a function, ?(𝑥), is the function 𝐹(𝑥) such that 𝐹 (𝑥) = ?(𝑥). Notation: ∫ 𝒇(𝒙)𝒅𝒙 = 𝑭(𝒙) + 𝑪 Basic Shortcut Rules 1) ∫ 𝑥 𝑛 ?𝑥 = 1 𝑛+1 𝑥 𝑛+1 + 𝐶 , 𝑛 ≠ −1 2) ∫ 𝑥 −1 ?𝑥 = ∫ 1 𝑥 ?𝑥 = ln |𝑥| + 𝐶 3) ∫ ? 𝑥 ?𝑥 = ? 𝑥 + 𝐶 Examples (Note that the Sum/Difference and Constant Multiple Rules still hold) 3 .
3)An object is tossed upwards from the top of a building at a starting height