When to Use Trigonometric Substitution?
We use trigonometric substitution in the following cases,
Expression | Substitution |
|---|---|
a2 + x2 | x = a tan θ |
a2 – x2 | x = a sin θ |
x2 – a2 | x = a sec θ |
[Tex]\sqrt{\frac{a-x}{a+x}} [/Tex] | x = a cos 2θ |
[Tex]\sqrt{\frac{x-\alpha}{\beta-x}} [/Tex] | x = α cos2θ + β sin2θ |
Trigonometric Substitution: Method, Formula and Solved Examples
Trigonometric Substitution is one of the substitution methods of integration where a function or expression in the given integral is substituted with trigonometric functions such as sin, cos, tan, etc. Integration by substitution is an easiest substitution method.
It is used when we make a substitution of a function, whose derivative is already included in the given integral function. By this, the function gets simplified, and simple integrals function is obtained which we can integrate easily. It is also known as u-substitution or the reverse chain rule. Or in other words, using this method, we can easily evaluate integrals and antiderivatives.
Trigonometric Substitution
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