In this video we will learn about one of trigonometric substitutions.We focus on Tangent substitution.
Trigonometric substitution is a technique used in calculus to simplify the integration of expressions involving square roots of quadratic forms. It leverages trigonometric identities to rewrite integrals into a form that is easier to handle.
General Procedure:
Identify the quadratic form in the square root (or elsewhere in the integral). Choose the appropriate trigonometric substitution based on the form. Rewrite the integral in terms of the trigonometric function using the substitution. Simplify using trigonometric identities. Evaluate the integral. Back-substitute the trigonometric function into the original variable using the relationships.
