For sqrt(x^2 + a^2), substitute x = a*tan(theta).For sqrt(a^2 – x^2), substitute x = a*sin(theta).Check out other posts:- Hyperbolic Trig Identity, Trig Reciprocal Identities With Formula. In some cases, it may more appropriate to use other techniques, such as partial fraction decomposition or substitution with substitution. It also important to note that trigonometric substitution not always the best method for evaluating integrals. Since the expression of the form √(a^2 – x^2), it can substituted with sinθ. Solution: Identify the expression that can substituted with a trigonometric function.Ĭhoose the appropriate trigonometric function based on the expression. Here some examples of how to use trigonometric substitution:Įxample 1: Evaluate the integral of √(9 – x^2) dx. These expressions often encountered when integrating functions that involve squares or square roots. It most useful when the integrand involves expressions that of the form √(a^2 – x^2), √(x^2 – a^2), or √(x^2 + a^2). There some general guidelines for when to use trigonometric substitution. Replace the expression with the corresponding trigonometric function and determine the value of θ.Ĭheck the solution to see if it the most simplified form possible. Choose the appropriate trigonometric function based on the expression. Identify the expression that can substituted with a trigonometric function. When making a trigonometric substitution, it important to remember the following steps: Where a is a constant, x is the variable being integrated, and θ is the angle whose cosecant is equal to x/a. Where a is a constant, x is the variable being integrated, and θ is the angle whose secant is equal to x/a.

Where a is a constant, x is the variable being integrated, and θ is the angle whose tangent is equal to x/a. Where a is a constant, x is the variable being integrated, and θ is the angle whose cosine is equal to x/a.

Where a is a constant, x is the variable being integrated, and θ is the angle whose sine is equal to x/a.

Inverse trig cheat sheet