mesduality Tag Posts Index

Integrals and Volumes by Cylindrical Shells: Example 4

In this video I go over another example on solving volumes using cylindrical shells. In this example I solve for the volume of the solid formed by rotating the region

Integrals and Work: Introduction

In this video I go over the concept of work in terms of the definition of work as the force multiplied by displacement (W = F·d) as well as defining it using integrals

Integrals and Work Example 1

In this video I go over 2 examples on determining the amount of work or energy required in performing an action. In this video first example the force is constant,

Integrals and Work: Example 2 - Hooke's Law

In this video I go over another example on work and this time deal with Hooke's Law. Hooke's Law states that the force required to maintain a spring stretched x

Infinite Sequences and Series: Representations of Functions as Power Series

In this video I go over further into infinite sequences and series; and in particular expand upon my earlier video on power series. This time I show how we can represent

Integrals and Work: Example 3 - Pulling a Rope

In this video I go over another example on determining the amount of work done in moving an object using integrals and this time I look at pulling a rope from the

Integrals and Work: Example 4 - Water Tank

In this video I go over another example on calculating work using integrals and solve for the amount of work required in pumping water out of an inverted circular

Integrals and Average Value of a Function

In this video I go over another video on the average value of a function and derive the formula for average value using integrals. This is important when averaging

Integrals and Average Value: Example 1

In this video I go over an example on solving for the average value of a function and solve the average value of the function y = 1 + x2 from x = - 1 and x = 2.

Mean Value Theorem for Integrals

In this video I go over the Mean Value Theorem for Integrals which states that for any continuous function from x = a to x = b there exists a number c in that interval

Mean Value Theorem for Integrals: Proof

In this video I go over the proof of the mean value theorem for integrals which I covered in my last video. The proof considers a function written as an integral

Mean Value Theorem for Integrals: Example 1

In this video I go over an example on using the mean value theorem for integrals to first show that there are 2 x-values that correspond to the average value of

🔥#MESScience 1: How Does a Powerball Gyroscope Work? + Gyros Are Inverted Pendulums (DTube)

In #MESScience 1, I introduce my latest video series: MES Science Tutorials and continue on my pursuit for understanding true gyroscope physics. Since conventional

🔥#MESScience 1: How Does a Powerball Gyroscope Work? + Gyros Are Inverted Pendulums

In #MESScience 1, I introduce my latest video series: MES Science Tutorials and continue on my pursuit for understanding true gyroscope physics. Since conventional

Integrals and Average Value: Example 2 Velocity

In this video I go over an example on average value and show that the average velocity when defined as the change in position over the change in time is equal to

Applied Project: Where to Sit at the Movies

In this video I go over another Applied Project problem and go about answering the problem of determining the best seat to sit at when at the movie theatre. The

Integration by Parts: Proof

In this video I go over the method of integration by parts which allows the ability to simplify a more complex function to make integration easier. The integration

Integration by Parts: Example 1

In this video I go over a pretty useful example on solving integrals by the method of integration by parts. The example I cover is the integral of the function x·sin(x)

Integration by Parts: Example 2

In this video I go over another example on solving integrals using the method of Integration by Parts. The example involves solving the integral of ln(x). Watch

Integration by Parts: Example 3: Integrating Twice by Parts

In this video I go over another example on the method of Integration by Parts. In this example I solve the integral of the function t2et and use the method of