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Overview The slope-intercept equation (y = mx + b) is a linear equation that gives both the slope of a line and where the line crosses the y-axis. It has many applications outside of mathematics, from construction and describing the grade of terrain to describing the results of scientific experiments if there is a linear […]
Overview Suppose we have an integral which appears unsolvable by ordinary means, such as ∫xsin(x)dx In many cases, we can do what is called integration by parts, which is where we split the equation we are taking the integral of into two parts, with the goal of simplifying the equation such that we can reduce […]
Overview Occasionally, you will have what are called composite functions; that is, functions that are composed of multiple functions and thus cannot be differentiated easily. In reality, although these may look tricky, they are actually fairly straightforward. Function composed of two functions Suppose we have an equation written as f(g(x)). Then d/dx f(g(x)) = f’(g(x))g’(x) […]
Overview Sometimes, a derivative is done using the chain rule, and it leaves with an equation that, at first glance, can look intractable when we are attempting to integrate it. In those cases, although the problem may look difficult or often will look like something that can only be solved through the use of Integration […]
Overview When the coefficient of the squared term is greater than 1, an extra step is added to factoring the trinomial. It can be factored by either using FOIL or a modified form of factoring by grouping. Factoring the Squared Term When the squared term of a quadratic trinomial is x2 with a coefficient of 1, […]