How to Evaluate Definite Integrals?

To find the definite integral of f(x) over interval [a, b] i.e.,we have following steps:

Step 1: Find the indefinite integral ∫f(x) dx.

Step 2: Evaluate p(a) and p(b) where, p(x) is the antiderivative of f(x), p(a) is the value of antiderivative at x = a, and p(b) is the value of antiderivative at x = b.

Step 3: Calculate p(b) – p(a).

The value obtained in Step 3 is the desired value of the definite integral.

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Definite Integrals are used to find areas of the complex curve, volumes of irregular shapes, and other things. Definite Integrals are defined by, let us take p(x) to be the antiderivative of a continuous function f(x) defined on [a, b] then, the definite integral of f(x) over [a, b] is denoted by and is equal to [p(b) – p(a)].

= p(b) – p(a)

The numbers a and b are called the limits of integration where a is called the lower limit and b is called the upper limit. The interval [a, b] is called the interval of the integration.

Note

• Constant of Integration is not included in the evaluation of the definite integral.
• is read as “integral of f(x) from a to b”