Trig substitution is a technique used in integration to solve integrals involving radical functions or expressions with quadratic terms. It involves replacing these expressions with equivalent trigonometric functions in order to simplify the integral.
Trig substitution is most useful when the integral involves a radical function such as √(a^2-x^2) or √(a^2+x^2). It can also be used when the integrand contains a quadratic term in the form of a^2-x^2 or a^2+x^2.
The three major trig substitutions used in integration are:
The trig substitution to use depends on the form of the integral. If the integrand contains a^2-x^2, then use the first substitution. If it contains a^2+x^2, use the second substitution. If it contains x^2-a^2, use the third substitution. It is also important to check if any other algebraic manipulations can be done to simplify the integral before using trig substitution.
Some common mistakes to avoid when using trig substitution include: