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Indefinite Integral Video Lecture | Calculus - Mathematics
FAQs on Indefinite Integral Video Lecture - Calculus - Mathematics
| 1. What is an indefinite integral? |  |
Ans. An indefinite integral, also known as an antiderivative, is a mathematical function that represents the reverse process of differentiation. It helps determine the original function when only the derivative is known.
| 2. How is an indefinite integral represented mathematically? | |
Ans. An indefinite integral is represented by ∫(f(x)) dx, where f(x) is the function to be integrated and dx represents the differential of x.
| 3. What is the significance of the constant of integration in an indefinite integral? | |
Ans. The constant of integration is added to the result of an indefinite integral. It arises because the derivative of a constant is always zero, and when integrating, we lose information about the constant term in the original function.
| 4. How can the power rule be applied to solve indefinite integrals? | |
Ans. The power rule states that for any constant n ≠ -1, the integral of x^n with respect to x is (x^(n+1))/(n+1) + C, where C represents the constant of integration.
| 5. Can all functions be integrated using indefinite integrals? | |
Ans. No, not all functions can be integrated using indefinite integrals. Some functions do not have an elementary antiderivative, and their integration requires advanced techniques such as integration by parts or substitution.
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