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Evaluation of Definite Integrals by Substitution

notes

One of the important methods for finding the indefinite integral is the method of substitution.
To evaluate `int_a^b f(x) dx`, by substitution, the steps could be as follows:

1. Consider the integral without limits and substitute, y = f (x) or x = g(y) to reduce the given integral to a known form. 

2. Integrate the new integrand with respect to the new variable without mentioning the constant of integration. 

3. Resubstitute for the new variable and write the answer in terms of the original variable. 

4. Find the values of answers obtained in (3) at the given limits of integral and find the difference of the values at the upper and lower limits. 

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Shaalaa.com | Integrals part 40 (Definite integral by substitution)

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Integrals part 40 (Definite integral by substitution) [00:12:20]
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