In this tutorial, we'll work through 2 different approaches to solving the integral of sin3(ax). Now, there maybe more ways of approaching this problem, but these were the most obvious to me. Using a

We can apply the principle of exponential decay to find equations that model the charge remaining in a capacitor as it is discharged through a resistor. The circuit diagram is shown below... When the switch

What I love about mathematics is some of the very creative and ingenious methods that someone has come up with to find solutions to perplexing problems. The integral of √(a2 - x2) is a great example one

Inasmuch as the differential equation dy/dx = ky models exponential growth, it follows that dy/dx = -ky models exponentially decaying processes. A exponential decay process, which is a slowing reduction

With the differential equation dy/dx = ky, we found the general solution to be y(x) = Aekx. We worked this out in my last post. This equation lends itself to the modelling of exponential growth. Now in

In this video, we work through the process of solving for the general solution of a simple separable differential equation: The general solution is obtained by separating the variables so that all y's

Differential Equations are one of the most useful tools developed in mathematics. You'll see them everywhere in Engineering, Physics, Biology, etc. for the modelling of phenomena. So what are differential

The term 1/(a2 + x2) is purely algebraic. However, its integral is trigonometric. When you look this up in a table of integrals, you'll find the integral: ∫1/(a2+x2)dx = (1/a)arctan(x/a) + C How is this

In this video, we work through the derivation of the reduction formula for the integral of cosn(x) or [cos(x)]n. The first step is to rewrite the integral as: ∫cosn(x)dx = ∫cosn-1(x)cos(x)dx Thus we have

In this video, I work through the steps to solving the integral of cos3(x) or [cos(x)]3. Note that because cos(x) is a function of x, not a mere polynomial, we can't just use the power formula as a method

Watch Derivatives of Exponents Part One - A Calculus Math Tutorial video on DTubeIn this excerpt from the derivatives of whole number exponents (1,2,3,4,5.....) are explained through geometry. This short

Watch Derivative of an Inverse Function - A Calculus Math Tutorial video on DTubeIn this excerpt from we show a derivative of a function which is an inverse of some original function. This short but very

Watch Derivatives of Functions Within Functions - A Calculus Math Tutorial video on DTubeExcerpt from In this brief video the derivatives of functions within functions are described through geometry. This

Watch Derivatives of Division - A Calculus Math Tutorial video on DTubeIn this excerpt from we show a derivative of a function that is composed of two divided functions is explained through geometry. This

Watch Derivatives of Multiplication - A Calculus Math Tutorial video on DTubeIn this excerpt from we show a derivative of a function that is composed of two multiplied functions is explained through geometry.

Watch Derivatives of Sin, Cos, Tan Trigonometry - A Calculus Math Tutorial video on DTubeIn this excerpt from a derivatives of trigonometric functions sin, cos, and tan are explained through geometry.

Watch Definition of Derivatives - A Calculus Math Tutorial video on DTubeIn this excerpt from the definition of the derivative is described through geometry. Derivatives are a basic concept of calculus

Watch Derivatives of Addition - A Calculus Math Tutorial video on DTubeIn this excerpt from we show a derivative of a function that is composed of two added functions is explained through geometry. This