Indefinite Integrals
Flashcard
•
Mathematics
•
11th - 12th Grade
•
Practice Problem
•
Hard
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1.
FLASHCARD QUESTION
Front
What is an indefinite integral?
Back
An indefinite integral represents a family of functions whose derivative is the integrand. It is expressed as ∫f(x)dx = F(x) + C, where F(x) is the antiderivative of f(x) and C is the constant of integration.
2.
FLASHCARD QUESTION
Front
What is the power rule for integration?
Back
The power rule states that ∫x^n dx = (1/(n+1))x^(n+1) + C, for n ≠ -1.
3.
FLASHCARD QUESTION
Front
Evaluate the indefinite integral: ∫ t⁶ dt
Back
1/7 t⁷ + C
4.
FLASHCARD QUESTION
Front
What does the constant of integration (C) represent in indefinite integrals?
Back
The constant of integration (C) represents the family of all antiderivatives of a function, accounting for the fact that the derivative of a constant is zero.
5.
FLASHCARD QUESTION
Front
Evaluate the indefinite integral: ∫ (3x² + 2) dx
Back
x³ + 2x + C
6.
FLASHCARD QUESTION
Front
What is the integral of a constant?
Back
The integral of a constant 'a' is ∫a dx = ax + C.
7.
FLASHCARD QUESTION
Front
Evaluate the indefinite integral: ∫ e^x dx
Back
e^x + C
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