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What is an Integral?

An integral is a fundamental concept in calculus that represents the accumulation of quantities. It can be thought of as the reverse of differentiation (finding the antiderivative) or as calculating the area under a curve.

There are two types of integrals: indefinite integrals (antiderivatives) which give a family of functions, and definite integrals which give a numerical value representing the signed area between a function and the x-axis over an interval.

Key Facts About Integrals

• •The integral of x^n is x^(n+1)/(n+1) + C (Power Rule)
• •The integral of 1/x is ln|x| + C
• •The integral of e^x is e^x + C
• •The integral of sin(x) is -cos(x) + C
• •The integral of cos(x) is sin(x) + C
• •Always add the constant of integration (+C) for indefinite integrals
• •Definite integrals use the Fundamental Theorem of Calculus: F(b) - F(a)
• •Integration is the inverse operation of differentiation

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