Integral (Power Rule) Calculator
Calculate the integral of a term ax^n using the power rule. Shows the antiderivative and definite integral.
Definite
54.0000
Formel
## Power Rule for Integration ### Rule **integral of ax^n dx = (a/(n+1)) × x^(n+1) + C** (when n ≠ -1) For n = -1, the integral is a × ln|x| + C. ### Definite Integral Evaluate the antiderivative at the upper and lower bounds and subtract: **F(upper) - F(lower)**
Lösungsbeispiel
Integrate 6x² from 0 to 3.
- 01Antiderivative: (6/3)x³ = 2x³
- 02F(3) = 2 × 27 = 54
- 03F(0) = 2 × 0 = 0
- 04Definite integral = 54 - 0 = 54
Häufig Gestellte Fragen
What is the power rule for integration?
The integral of x^n is x^(n+1)/(n+1) + C, valid for all n except -1. This reverses the power rule for derivatives.
What is + C in indefinite integrals?
C is the constant of integration. Since the derivative of any constant is 0, the antiderivative includes an unknown constant.
What happens when n = -1?
When n = -1, the integral of 1/x is ln|x| + C (the natural logarithm). The power rule formula does not apply because it would involve division by zero.
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