Indefinite Integrals Flashcard

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 and C is the constant of integration.

Front

What does the constant 'C' represent in an indefinite integral?

Back

The constant 'C' represents an arbitrary constant that accounts for all possible antiderivatives of a function.

Front

Evaluate the indefinite integral: ∫ 6x(x² + 1)² dx

Back

(x² + 1)³ + C

Front

Evaluate the indefinite integral: ∫ t⁶ dt

Back

1/7 t⁷ + C

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.

Front

What is the integral of a constant 'a'?

Back

The integral of a constant 'a' is ∫a dx = ax + C.

Front

What is the integral of e^x?

Back

The integral of e^x is ∫e^x dx = e^x + C.

Front

What is the integral of sin(x)?

Back

The integral of sin(x) is ∫sin(x) dx = -cos(x) + C.

Front

What is the integral of cos(x)?

Back

The integral of cos(x) is ∫cos(x) dx = sin(x) + C.

Front

What is the substitution method in integration?

Back

The substitution method involves changing the variable of integration to simplify the integral, often using u-substitution.