Definite Integral Calculator — ∫ f(x)dx Numerically
Quick answer: Select a function, enter lower and upper bounds, and get ∫ₐᵇ f(x)dx via Simpson's Rule.
Calculate the definite integral ∫ₐᵇ f(x)dx for common functions using Simpson's Rule with 1,000 intervals. The result represents the net area under the curve from a to b. Works for x², x³, √x, sin, cos, ln, eˣ, and 1/x.
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Last reviewed: April 2026Report an error
Numerical definite integral ∫ₐᵇ f(x)dx using Simpson's Rule (1000 intervals).
∫ f(x)dx from 0 to 3
9
∫₍0₎^₍3₎ x² dx ≈ 9. Computed using Simpson's Rule with 1000 intervals.
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How to Use This Integral Calculator Calculator
- 1Select the function f(x).
- 2Enter the lower bound a.
- 3Enter the upper bound b.
- 4Read the definite integral (area under the curve from a to b).
Frequently Asked Questions
- The definite integral ∫ₐᵇ f(x)dx represents the net signed area between the function and the x-axis, from x=a to x=b. Positive where f(x)>0, negative where f(x)<0.
- A numerical integration method that approximates the integral by fitting parabolas to segments of the function. More accurate than the trapezoidal rule. Error ≈ O(h⁴).
- ∫₀³ x² dx = [x³/3]₀³ = 27/3 − 0 = 9. The calculator should return ≈ 9.000 confirming the formula.
- A definite integral ∫ₐᵇ f(x)dx gives a number (area). An indefinite integral ∫f(x)dx gives a function + C (the antiderivative).
- When f(x) is below the x-axis, the integral is negative. The total integral is net area = positive area minus negative area.
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