Indefinite Integrals

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.

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

Evaluate ∫ t⁶ dt.

Back

1/7 t⁷ + C

Front

Evaluate ∫(4 - 18x)dx.

Back

F(x) = 4x - 9x² + C

Front

What is the constant of integration?

Back

The constant of integration (C) represents an arbitrary constant added to the antiderivative, accounting for all possible vertical shifts of the function.

Front

Evaluate ∫ 5 dx.

Back

5x + C

Front

What is the integral of a constant?

Back

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

Front

Evaluate ∫ (3x² + 2x + 1) dx.

Back

x³ + x² + x + C

Front

What is the integral of e^x?

Back

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

Front

Evaluate ∫ sin(x) dx.

Back

-cos(x) + C