免费幂法则积分计算器
使用幂法则计算多项式函数的不定积分。
Definite
54.0000
New Coeff2.000000
New Exp3
公式
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
Definite Integral
Evaluate the antiderivative at the upper and lower bounds and subtract:
F(upper) - F(lower)
计算示例
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
常见问题
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.
学习