sg001 said:
U substitution is a technique used to simplify the process of integration by substituting a complex expression with a new variable. This helps to transform the integrand into a more manageable form, making it easier to solve.
To perform u substitution with limits, you first need to substitute the variable in the limits as well. Then, integrate the new expression with respect to the substituted variable. Finally, substitute back the original variable in the limits to get the final answer.
No, u substitution is not always necessary in integration. It is a useful technique for solving integrals involving complicated expressions or functions, but it may not always be the most efficient method.
Yes, u substitution can be used for definite integrals. However, the substitution must also be made in the limits of integration and taken into account when evaluating the integral.
One limitation of u substitution is that it may not always work for all integrals. There are certain integrals that cannot be solved using this technique, and other methods such as integration by parts may be necessary.