Polynomial interval
Evaluate integral from 0 to 2 of x^2 dx
Method: Use the Fundamental Theorem of Calculus.
- 1An antiderivative is x^3/3.
- 2Evaluate it at 2 and at 0.
- 3Subtract the lower endpoint value.
Final answer
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Definite Integral Calculator
Evaluate an integral between lower and upper bounds and receive an exact result without an integration constant.
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How to Use the Definite Integral Calculator
1
Enter the function and bounds
Write an expression followed by from a to b.
2
Find an antiderivative
The solver integrates the function symbolically.
3
Apply the bounds
Upper and lower values are substituted and subtracted.
Example
How the Definite Integral Calculator Chooses a Method
Evaluate an integral between two bounds and see how endpoint substitution produces the exact value.
A definite integral is evaluated by finding an antiderivative when possible and applying F(b)-F(a). The sign records net accumulation, so area below the x-axis contributes negatively unless total geometric area is requested.
Supported problem types
- Exact polynomial and elementary-function integrals
- Finite lower and upper bounds
- Signed accumulation over a closed interval
Limits and assumptions
- An improper integral requires a limit and may diverge.
- Discontinuities inside the interval must be handled as separate improper integrals.
Worked Definite Integral Calculator Examples
Each example names the method, shows the ordered reasoning, and keeps the final answer separate so you can check your own work.
Trigonometric interval
Evaluate integral from 0 to pi of sin(x) dx
Method: Use -cos(x) as an antiderivative.
- 1Find F(x)=-cos(x).
- 2Compute F(pi)=1 and F(0)=-1.
- 3Subtract to obtain 2.
Final answer
Reversed bounds
Evaluate integral from 3 to 1 of 2x dx
Method: Keep the bound order when applying F(b)-F(a).
- 1An antiderivative is x^2.
- 2Compute F(1)-F(3).
- 3The reversed interval makes the result negative.
Final answer
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What the Definite Integral Calculator Helps You Understand
Evaluate an integral between lower and upper bounds and receive an exact result without an integration constant.
Learning focus 1
Write an expression followed by from a to b.
Learning focus 2
The solver integrates the function symbolically.
Learning focus 3
Upper and lower values are substituted and subtracted.
Input tips
- • Write an expression followed by from a to b.
- • A definite integral evaluates a fixed difference, so the integration constants cancel.
Common mistakes to avoid
- • Adding +C to a bounded integral result.
- • Reversing the upper and lower endpoint subtraction.
Frequently Asked Questions
Why is there no + C?
A definite integral evaluates a fixed difference, so the integration constants cancel.
Can I use pi as a bound?
Yes. Enter pi directly, for example sin(x) from 0 to pi.
Should I add +C to a definite integral?
No. The constant cancels in F(b)-F(a), so a bounded integral has a numeric or exact expression as its result.
Can a definite integral be negative?
Yes. It measures signed accumulation; portions below the axis count negatively.