Indefinite Integral
Definition
An indefinite integral is the reverse process of differentiation. It represents a family of functions that have the same derivative.
Related terms
Definite Integral: The definite integral calculates the exact area under a curve between two points.
Antiderivative: An antiderivative is another term for an indefinite integral. It represents a family of functions that have the same derivative.
Fundamental Theorem of Calculus: This theorem connects differentiation and integration by stating that if F(x) is an antiderivative of f(x), then ∫f(x) dx from a to b equals F(b) - F(a).
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Practice Questions (8)
- Which of the following is an example of an indefinite integral?
- Evaluate the indefinite integral: ∫(5cos(x) + 2x) dx.
- Determine the indefinite integral of 6e^x + 2sin(x).
- Evaluate the indefinite integral: ∫(3x² + 2√(x)) dx.
- Evaluate the indefinite integral: ∫(5e^x - 2cos(x)) dx.
- Determine the indefinite integral: ∫(2cos(x) + 4/x²) dx.
- Evaluate the indefinite integral: ∫(2e^x - 3sin(x)) dx.
- What does the indefinite integral of the acceleration vector-valued function with respect to time give us?
