Integration by substitution is a technique used to solve integrals by replacing the variable with another variable or expression. This allows us to simplify the integral and make it easier to solve.
Integration by substitution is useful because it allows us to solve integrals that cannot be solved using other techniques. It also helps us to solve integrals that would be very difficult to solve using other methods.
Integration by substitution is typically used when the integral contains a function that can be simplified by replacing the variable with another expression. This can also be identified by looking for a pattern in the integral, such as a function and its derivative.
The process for solving an integration by substitution problem involves identifying the function to be replaced, choosing a suitable substitution, finding the derivative of the substitution, substituting the new variables into the integral, and then solving the resulting integral.
One common mistake to avoid when using integration by substitution is forgetting to change the limits of integration after substituting in the new variables. It is also important to check that the substitution is valid and that the resulting integral can be easily solved.