3 Important Methods of Integration To Know
U-Substitution, Integration by Parts, Trigonometric Substitution
One of the most essential parts of Calculus, integration details the techniques of finding an antiderivative, F(x), of the function f(x). It has many applications both in mathematics and physics that involve volume, area, and mechanics. In this article, we’ll examine three of the key methods for integration to have in your arsenal.
Integration is essentially the opposite of differentiation. The variety of difficulty within the subject of integration is extremely extensive, with some problems taking 5 seconds to solve and some problems taking 5 minutes. For example, we know that the derivative of x³ is 3x². Therefore, when we integrate 3x², we get x³+C. It is always important to remember the +C, since the derivative of a constant is always zero, so any constant value can be tacked on to the end of a derivative expression and differentiating will yield the same result.
However, not all problems are as simple as finding the integral of 3x². What is the integral of sin(2x)? One may jump to write down -cos(2x) + C, but sadly, this would be incorrect. The reasoning behind why this solution is incorrect leads us into our first method of integration: U-Substitution.
