Integration by Substitution
What is Integration by Substitution?
Integration by substitution is the method of finding the integration of the complex function where the normal techniques of integration fail. In this method, we find the substitute part of the function with another function and then get the transformed function which can be easily integrated.
How to Integrate by Substitution?
We can easily integrate any function of the form,
∫ f(g(x)).g'(x).dx
by just simply substituting g(x) = t and then replacing g'(x).dx = dt. So the function becomes ∫f(t)dt which can be easily integrated.
Why we use the substitution method?
We use integration by substitution to find the solution of the given function where the normal integration techniques fail.
How to know when to use Integration by Substitution?
We use integration by substitution when the given integration is of form ∫ f(g(x)).g'(x).dx or can be easily changed to the above form.
What are some situations where Integration by Substitution is used?
Some conditions where we use integration by substitution are,
- If the given function is in form f(√(a2 – x2)) we use substitution as, x = a sin θ or x = a cos θ
- If the given function is in form f(√(x2 + a2)) we use substitution as, x = a tan θ or x = a cot θ
Integration by Substitution Method
Integration by substitution is one of the important methods for finding the integration of the function where direct integration can not be easily found. This method is very useful in finding the integration of complex functions. We use integration by substitution to reduce the given function into the simplest form such that its integration is easily found.
In calculus, integration by substitution is a method used to solve integrals and antiderivatives, also referred to as u-substitution, the reverse chain rule, or change of variables. It serves as the analog to the chain rule used in differentiation. Essentially, this method can be viewed as the chain rule in reverse to simplify and evaluate integrals.
Now let’s learn more about the integration by substitution method, Integration by Substitution examples, and others in this article.
Table of Content
- What Is Integration by Substitution?
- Integration by Substitution Method
- When to use Integration by Substitution?
- Steps to Integration by Substitution
- Integration by Substitution – Important Substitutions
- Integration by Substitution Examples
- Integration by Substitution Questions
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