To evaluate definite integral, by substitution method, the following steps could be needed for evaluating the value of \(\int^b_a\) f(x) dx.
Step 1. Consider the integral without limits and substitute, y = f(x) or x = g{y) to reduce the given integral to a known form.
Step 2. Integrate the new integrand w.r.t. the new variable without mentioning the constant of integration.
Step 3. Resubstitute for the new variable and write the answer in terms of the original variable.
Step 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.
Remark:
After performing steps 1 and 2, there is no need of step 3. Here, the integral will be kept in the new variable itself, and the limits of the integral will accordingly be changed so that we can perform the last step.
