Definite Integrals

Question 1: What are definite integrals?

Answer:

Definite integrals are integrals that are defined under limits i.e., upper and lower limits. It is represented aswhere a is the lower limit and b is the upper limit of integration.

Question 2: How are definite integrals evaluated?

Answer:

For evaluating definite integrals following steps are followed:

• Find the indefinite integral ∫f(x)dx.
• 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.
• Calculate p(b) – p(a).
• The resultant is the desired value of the definite integral.

Question 3: Write the formula for definite integrals.

Answer:

Let p(x) be the antiderivative of function f(x) defined in the interval [a, b] then, the definite integral is given by:

= p(b) – p(a)

Question 4: What does the result of definite integral represent?

Answer:

The result obtained by solving the definite integral represents the area under the curve that is evaluated.

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”