“How Do You Integrate sin(x)cos(x)? – Maths Q&A”. (or powers of these roots), where a is a constant and u is an expression in x. This method works when the integrand contains radicals of the forms 2 ⭐ “Integration By Parts Intro (Video) | Khan Academy”. “Integration By Parts – Formula, ILATE Rule & Solved Examples”. “How To Do Integration By Parts – Dummies”. If you remember that, you can easily remember that the integral on the right is just like the one on the left, except with the u and v reversed. Here’s the formula: 3ĭon’t try to understand this yet. The basic idea of integration by parts is to transform an integral you can’t do into a simple product minus an integral you can do. Integrating by parts is the integration version of the product rule for differentiation. ⭐ “𝘶-Substitution Intro (Video) | Khan Academy”. “Integration Using Substitution Method (Solved Problems)”. “Integration By Substitution – Wikipedia”. Let’s look at an example problem together. Now it should be apparent to us why integrating sin(2x) doesn’t simply yield -cos(2x). It is absolutely necessary to “account” for the chain rule in both differentiation and integration problems. In examples like this, we say that the derivative of the function f(g(x)) is f’(g(x))*g’(x). This is why the derivative of -cos(2x) isn’t just sin(2x): we are missing an extra factor of 2 from the derivative of the inside function 2x. Īs I was taught, U-Substitution is a way of dealing with the chain rule from differentiation: It reverses it! The chain rule deals with derivatives of composite functions. “Calculus Workbook For Dummies Cheat Sheet – Dummies”.
Here are some integration rules and cheat sheets to assist you when learning and performing integral calculus.
Also, don’t forget to understand the Fundamental Theorem of Calculus!
This is a good starting place for your edification, not for the fainthearted and remember MATH IS FUN. I do not normally provide examples, but integration requires a great deal of time to recognize the various types and the methods to solve them. On this page, I provide examples of U-Substitution, Integration By Parts and Trigonometric Substitution.
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