Indefinite Integrals, Antiderivatives, Power Rule, Trig, Inverse, Log, Exp, Examples - Calculus

An indefinite integral, also known as an antiderivative, is a function whose derivative is the original function. It represents a family of functions that differ by a constant, which is included as a "+ C" in the final result, denoted by the integral symbol (∫) followed by the function and a differential (like dx). For example, the indefinite integral of f(x) is F(x) + C, where F'(x) = f(x).

💡Key Characteristics
• Antiderivative: It is the inverse operation of differentiation.
• Constant of Integration (+ C): This constant is crucial because the derivative of any constant is zero.
• No Fixed Boundaries: Unlike definite integrals, indefinite integrals do not have upper and lower limits of integration.
• Symbolic Representation: The notation ∫f(x)dx means "find the antiderivative of f(x)". The "dx" indicates the variable of integration and is the differential form of the function.

💡Example
To find the indefinite integral of f(x) = x²:
• Recall the power rule for integration: ∫xⁿ dx = xⁿ⁺¹/(n+1) + C.
• Apply the rule to x²: ∫x² dx = x²⁺¹/(2+1) + C = x³/3 + C.
• The result, x³/3 + C, represents all functions whose derivative is x², such as x³/3, (x³/3) + 5, or (x³/3) - 10.

💡Worksheets are provided in PDF format to further improve your understanding:
• Questions Worksheet: https://drive.google.com/file/d/1nyZAxMFIv3phTs8a9uQiZ7WKvrQ4fBKt/view?usp=drive_link
• Answers: https://drive.google.com/file/d/16wbbNzLH-O0LGu6SEvM5Nq9gNQlpoR-H/view?usp=drive_link

💡Chapters:
00:00 Indefinite integrals, power rule
01:28 Elementary antiderivatives
02:40 Antiderivatives of tan, cot, sec, cosec
04:15 Antiderivatives of inverse trig functions
05:34 Antiderivatives of log and exponential functions
07:00 Worked examples

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