Math & Algebra Tool
Integral Calculator
Calculate definite integral of f(x) = x².
Definite Integral
∫ x² dx
Frequently Asked Questions
What is an integral?+
An integral essentially calculates the total accumulation of a quantity. Geometrically, the definite integral represents the signed area between the function's graph and the x-axis.
What is the difference between Definite and Indefinite integrals?+
An Indefinite Integral (antiderivative) is a function (like F(x) + C). A Definite Integral returns a specific number representing the accumulated value between two points [a, b].
What is the Fundamental Theorem of Calculus?+
It links differentiation and integration. It states that to calculate a definite integral, you can find the antiderivative F(x) and compute F(b) - F(a).
What is 'C' in integration?+
C is the 'Constant of Integration'. Because the derivative of any constant is zero, we lose that information when differentiating. When integrating back, we add +C to represent any possible original constant.
How do integrals relate to physics?+
Work is the integral of Force over distance. Displacement is the integral of Velocity over time. Center of mass and moment of inertia are also calculated using integrals.
What is area under the curve?+
It is the primary geometric interpretation of the definite integral. If f(x) is positive Use this tool to find exactly how much space is 'under' the graph.