The concept of integral using substitution is a method used to simplify and solve integrals by substituting a variable with another expression. This allows for a more manageable integral that can be easily solved using basic integration techniques.
Substitution is most useful when the integrand (the expression inside the integral) contains a complicated or nested function. By substituting a variable with a simpler expression, the integral can be simplified and solved more easily.
The substitution variable should be chosen in a way that will make the integral easier to solve. This often involves choosing a variable that will cancel out or simplify parts of the integrand, such as using u to replace sin x or ex.
Yes, there are some general rules that can be followed when using substitution in integrals. These include substituting for a term with a power, substituting for a trigonometric function, and using parentheses when needed to avoid errors.
No, substitution is not always applicable to all integrals. It is most effective for integrals with a single variable and can also be used for definite integrals. However, it may not work for integrals with multiple variables or improper integrals.