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latest #dtube-calculus created topics | Ecency

masterwu

2017-10-07 09:16

DTube: Integral of sin^3(x), sin^3(ax) with substitution and trigonometric identity

DTube: Integral of sin^3(x), sin^3(ax) with substitution and trigonometric identity

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

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masterwu

2017-09-27 12:45

DTube: The math behind your Camping Torch with dy/dx = -ky

DTube: The math behind your Camping Torch with dy/dx = -ky

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

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masterwu

2017-09-25 04:31

DTube: Integral of ∫√(a^2 - x^2)dx using a Trigonometric Substitution

DTube: Integral of ∫√(a^2 - x^2)dx using a Trigonometric Substitution

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

masterwu

2017-09-23 06:11

DTube: Modelling the Decay of Nuclear Medicine with dy/dx = -ky

DTube: Modelling the Decay of Nuclear Medicine with dy/dx = -ky

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

onemoretea

2026-08-11 21:27

Boats, a Cloud and Gorgeous Reflections - My Actifit Report Card: August 11th, 2026

Boats, a Cloud and Gorgeous Reflections - My Actifit Report Card: August 11th, 2026

Welcome to Liquid Eye’s Actifit Blog Tuesday ☀️ 10593 A crisp Tuesday morning for a lovely, leisurely interval-walking route across several bridges, past a motley collection of boats and magnificent

masterwu

2017-09-20 03:50

DTube: Modelling Exponential Growth of Bacteria with dy/dx = ky

DTube: Modelling Exponential Growth of Bacteria with dy/dx = ky

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

masterwu

2017-09-17 05:42

DTube: Separable Differential Equations: dy/dx = ky

DTube: Separable Differential Equations: dy/dx = ky

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

masterwu

2017-09-13 12:12

DTube: Introduction to Differential Equations

DTube: Introduction to Differential Equations

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

masterwu

2017-09-12 15:12

DTube: Integral of ∫1/(a^2 + x^2)

DTube: Integral of ∫1/(a^2 + x^2)

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

apnigrich

2026-08-13 21:01

Poseidon's Trident

Poseidon's Trident

Poseidon's Trident

[] This is my application for the contest Reflection Hunters Contest - SMARP (Show Me A Reflection Picture) ~ Round 284 🎺 Announcement 🎺 by @olgavita @olgavita, How's it going? Have you seen the Captain

masterwu

2017-09-11 15:26

DTube: Reduction Formula for Integral of ∫cos^n(x)dx

DTube: Reduction Formula for Integral of ∫cos^n(x)dx

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

masterwu

2017-09-09 10:25

DTube: Integral of ∫cos^3(x)dx

DTube: Integral of ∫cos^3(x)dx

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

eroavromninocule

2017-08-19 11:29

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Derivatives of Exponents Part One - A Calculus Math Tutorial

Derivatives of Exponents Part One - A Calculus Math Tutorial

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

eroavromninocule

2017-08-19 11:23

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Derivative of an Inverse Function - A Calculus Math Tutorial

Derivative of an Inverse Function - A Calculus Math Tutorial

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

vscampbell

2026-08-10 17:10

Stop Running the Business. Get Back to the Work You Love.

Stop Running the Business. Get Back to the Work You Love.

source You didn’t start your business to run a business. You started it because you love the work. Somewhere along the way, email, scheduling, admin, and client follow-up started eating the hours that

eroavromninocule

2017-08-19 11:17

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Derivatives of Functions Within Functions - A Calculus Math Tutorial

Derivatives of Functions Within Functions - A Calculus Math Tutorial

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

eroavromninocule

2017-08-19 11:11

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Derivatives of Division - A Calculus Math Tutorial

Derivatives of Division - A Calculus Math Tutorial

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

eroavromninocule

2017-08-19 11:06

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Derivatives of Multiplication - A Calculus Math Tutorial

Derivatives of Multiplication - A Calculus Math Tutorial

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.

eroavromninocule

2017-08-19 11:00

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Derivatives of Sin, Cos, Tan Trigonometry - A Calculus Math Tutorial

Derivatives of Sin, Cos, Tan Trigonometry - A Calculus Math Tutorial

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.

steven-patrick

2026-08-14 14:27

A proper garden tour

A proper garden tour

Today I thought I would do a proper garden tour. I talk about the garden alot but haven't done a post on it recently.

eroavromninocule

2017-08-19 10:55

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Definition of Derivatives - A Calculus Math Tutorial

Definition of Derivatives - A Calculus Math Tutorial

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

eroavromninocule

2017-08-19 10:50

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Derivatives of Addition - A Calculus Math Tutorial

Derivatives of Addition - A Calculus Math Tutorial

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