曲线下面积计算器 — 公式
## Area Under a Curve
### Definite Integral
The area under y = ax^n from x₁ to x₂ is:
**Area = |integral from x₁ to x₂ of ax^n dx|**
**= |(a/(n+1)) × [x₂^(n+1) - x₁^(n+1)]|**
### Average Value
The average value of f on [x₁, x₂] is:
**f_avg = (1/(x₂ - x₁)) × integral of f(x) dx**
### Definite Integral
The area under y = ax^n from x₁ to x₂ is:
**Area = |integral from x₁ to x₂ of ax^n dx|**
**= |(a/(n+1)) × [x₂^(n+1) - x₁^(n+1)]|**
### Average Value
The average value of f on [x₁, x₂] is:
**f_avg = (1/(x₂ - x₁)) × integral of f(x) dx**
计算示例
Find the area under y = x² from x = 0 to x = 4.
- Antiderivative: x³/3
- F(4) = 64/3 ≈ 21.3333
- F(0) = 0
- Area = 21.3333 - 0 = 21.3333
- Average value = 21.3333 / 4 ≈ 5.3333