Substitution in integral is a technique used to simplify and solve integrals by replacing a variable with a different expression. This is also known as the u-substitution method.
Substitution in integral is most useful when the integrand contains a function that is difficult to integrate, such as trigonometric functions or exponential functions.
The substitution variable, usually denoted as u, should be chosen in a way that simplifies the integral. This can be done by looking for patterns or using trigonometric identities.
The steps for substitution in integral are as follows: 1. Identify the substitution variable u. 2. Rewrite the integrand in terms of u. 3. Calculate du/dx. 4. Substitute the new expression for u and du into the integral. 5. Integrate the new expression with respect to u. 6. Substitute back in the original variable.
Substitution in integral may not always work, especially when the integrand does not have a clear substitution variable. It is important to also consider other methods, such as integration by parts, when solving more complex integrals.