Calculus
Definite Integral Calculator
Evaluate definite integrals with bounds. Compute the definite integral of a function over a closed interval [a, b] using the Fundamental Theorem of Calculus.
d/dx
Examples:
Differentiation Rules
Power Rule
d/dx [x^n] = nx^(n-1)
Product Rule
[fg]' = f'g + fg'
Chain Rule
d/dx [f(g(x))] = f'(g(x))g'(x)
Constant Rule
d/dx [c] = 0
Share & Embed
Share your exact result or embed this tool.
Solution Methodology
01
Enter Function & Bounds
Input f(x) and the integration limits a and b.
02
Find Antiderivative
Compute F(x) = ∫f(x) dx symbolically, showing the integration rule applied.
03
Evaluate F(b) − F(a)
Substitute the bounds and simplify to produce the definite integral value.
Common Questions
How do you evaluate a definite integral?
Find the antiderivative F(x) of the integrand f(x), then substitute the upper and lower bounds: the answer is F(b) − F(a). This is the First Fundamental Theorem of Calculus and converts the continuous summation into a simple subtraction.
What does a definite integral represent geometrically?
It represents the net signed area between the function and the x-axis over [a, b]. Regions above the x-axis contribute positive area; regions below contribute negative area. If the function crosses the x-axis, the integral may be smaller than the total enclosed area.