Free Online
Definite Integral Calculator
Calculate the area under the curve in seconds. Accurate, fast, and easy to use.
Why Use Our Definite Integral Tool?
We make calculating definite integrals simple and precise.
Instant Calculation
Get the numerical value or exact symbolic result instantly.
High Precision
Uses advanced algorithms to ensure accurate results for any limits.
Visual Learning
Understand the concept of area accumulation under the curve.
What is a Definite Integral?
A definite integral has start and end values, called the lower and upper limits (or bounds). It calculates the net area between the function f(x) and the x-axis over the interval [a, b].
According to the Fundamental Theorem of Calculus, if F(x) is the antiderivative of f(x), then:
The result of a definite integral is a number, unlike an indefinite integral which returns a function.
Geometric Interpretation
Geometrically, the definite integral represents the signed area under the curve.
- If the curve is above the x-axis, the area is positive.
- If the curve is below the x-axis, the area is negative.
- The total definite integral is the sum of these signed areas.
How to Use This Calculator
- 1Enter the function f(x).
- 2Enter the lower limit (a) and upper limit (b). These can be numbers or expressions like 'pi'.
- 3Click "Calculate Solution" to find the value.
Frequently Asked Questions
What if the limits are infinity?
This is called an improper integral. Our calculator can often handle these if the integral converges.
Can the result be negative?
Yes, if the area below the x-axis is larger than the area above it, the result will be negative.
Do I need to add + C?
No, for definite integrals, the constant of integration cancels out (C - C = 0).
Is this calculator free?
Yes, it is completely free to use.