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Properties of Indefinite Integrals Video Lecture | Mathematics (Maths) Class 12 - JEE

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FAQs on Properties of Indefinite Integrals Video Lecture - Mathematics (Maths) Class 12 - JEE

1. What is the definition of an indefinite integral?
Ans. An indefinite integral, also known as an antiderivative, is a mathematical operation that calculates the general formula for a family of functions whose derivative is equal to a given function.
2. How is the symbol for an indefinite integral written?
Ans. The symbol for an indefinite integral is ∫, which represents the integral sign. It is followed by the function to be integrated and then a differential symbol, such as dx.
3. Can the constant of integration be omitted when finding an indefinite integral?
Ans. No, the constant of integration should be included when finding an indefinite integral. This constant accounts for all possible antiderivatives of a given function and is represented by "+ C" at the end of the integral.
4. What is the relationship between the derivative and the indefinite integral?
Ans. The relationship between the derivative and the indefinite integral is described by the Fundamental Theorem of Calculus. It states that if F(x) is an antiderivative of f(x), then the indefinite integral of f(x) is equal to F(x) + C, where C is the constant of integration.
5. How can the power rule be applied to find indefinite integrals?
Ans. The power rule can be applied to find indefinite integrals by raising the variable to the next power and dividing by that power. For example, the indefinite integral of x^n is (x^(n+1))/(n+1) + C, where C is the constant of integration.
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