Area Under Curve Calculator
Calculate the area under y = ax^n between two x-values using the definite integral.
Area
21.3333
Y At X10.0000
Y At X216.0000
Avg Value0.0000
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
Example Calculation
Find the area under y = x² from x = 0 to x = 4.
- 01Antiderivative: x³/3
- 02F(4) = 64/3 ≈ 21.3333
- 03F(0) = 0
- 04Area = 21.3333 - 0 = 21.3333
- 05Average value = 21.3333 / 4 ≈ 5.3333
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