Find an indefinite antiderivative or evaluate a definite integral between two bounds. Results include a simplified symbolic expression, an independent numeric check for definite integrals, and a graph of the function over the interval.
Formula
The Fundamental Theorem of Calculus connects antiderivatives and definite integrals:
if F′(x) = f(x), then ∫[a,b] f(x) dx = F(b) − F(a)
An indefinite result includes + C because all functions differing by a
constant have the same derivative.
Examples
Integrate x²
The indefinite integral of x² is x³/3 + C. From 0 to 3, its definite integral is 9.
Integrate sin(x)
An antiderivative of sin(x) is −cos(x). From 0 to π, the definite integral is 2.
A negative definite result represents net signed area. Use
the graph to see where the function lies above or below the x-axis.