Author Archives: hangtime

Average Value Word Problems

These problems use the same formula and steps as the ones in the previous video, except they're buried in word problems about average speed or average flow or average price. If a problem contains the word "average", you're probably looking at one of these.

This video appears on the page: Average Value & Mean Value Theorem

Average Value and The Mean Value Theorem

These problems are all the same pretty much: they either want you to find the average value, or they want you to find the "c" on the interval [a,b] at which the value of the function is equal to the average value of the function. That wasn't clear enough? You should watch this video!

This video appears on the page: Average Value & Mean Value Theorem

Average Value & Mean Value Theorem
Average Value and The Mean Value Theorem
Average Value Word Problems

Finding the average value of a function on an interval, word problems, plug-and-chug.

Part of the course(s): ,Test Image Problem ,Calculus

U-Substitution of Logs & Exponentials

We've already hit some ln|u| integrals in prior videos, but in this one we'll cover tricky problems where ln is inside a Power Rule problem, or exponentials are within rational functions. These are hard, but they'll take your game to the next level!

This video appears on the page: U-Substitution Integration

U-Substitution of Trig Functions

Usually in U-sub problems, there's not a lot of drama in picking your u and du. It's fairly obvious. But trig functions are extra-tricky because teachers design problems that can be worked more than one way, or that take a lot of cleverness in picking your u and du to even get them to work. I also work a few examples that require the trig identities you'll need for calculus.

This video appears on the page: U-Substitution Integration

U-Substitution of Rational Functions

Rational functions are the big fractions with x's upstairs and down, but they come in many flavors. In this video I work rational examples with the Power Rule, arcsin and arctan, and tougher algebraic problems requiring tricky tricks before you can integrate. This video even covers a couple integrations that require synthetic division and polynomial long division!

This video appears on the page: U-Substitution Integration

U-Substitution with Roots & Radicals

These are really just a sub-genre of the Power Rule, but they do have a lot of different algebra due to all the fractional exponents, so they get their own video! Including algebraic tricks to use when your u and du "don't match".

This video appears on the page: U-Substitution Integration

U-Substitution & The Power Rule

The most common type of U-sub problem is the power rule, since power rules come in so many different flavors: polynomials, exponents, fractions, roots... So this video takes you through examples of all the types, and some hard ones too, to get you used to this crazy U-sub stuff. Practice practice practice!

This video appears on the page: U-Substitution Integration

How your teacher will make you show your work

There are a few different ways to work U-Substitution problems. They all get the same result, yet many calculus teachers real sticklers for you writing the steps exactly how they want you to. So my job, in this video, is to show you the most common ways of doing this, so that you'll be able to do it just like your teacher wants you to!

This video appears on the page: U-Substitution Integration

What the heck is U-Substitution

U-Sub is really the Chain Rule in reverse, but it's difficult and more abstract. So in this video I work a couple examples, but mostly it's about showing you how U-sub is reverse chain rule, and how that can help you to understand what's going on.

This video appears on the page: U-Substitution Integration

U-Substitution Integration:
Power Rule & Exponents
Roots & Radicals
Trig Functions
Exponentials
Logs

This chapter covers U-substitution with all the major integral types: power rule, roots, radicals, rational functions, fractions, exponentials, logs, trig functions.

Part of the course(s): ,Test Image Problem ,Calculus

Integral Properties

This is a quick video about how you can manipulate integrals. Kind of like exponent rules and log properties, definite integrals can be combined, added, subtracted, etc. in a specific type of problem I'll show you that most teachers use.

This video appears on the page: Definite Integrals

Positive vs Negative Area

Strangely, even though area can't be negative in the physical world, it happens with integrals all the time. This video is all about when to worry about that, when it's okay, and how to make it better.

This video appears on the page: Definite Integrals

Definite Integrals & The Fundamental Theorem of Calculus

These things may have intimidating names, but they're about the easiest thing you're going to see this year! For the sake of non-confusion, we won't be using U-substitution on these.

This video appears on the page: Fundamental Theorem of Calculus ,Definite Integrals

Definite Integrals
Definite Integrals & The Fundamental Theorem of Calculus
Positive vs Negative Area
Integral Properties

In this chapter we use The Fundamental Theorem of Calculus and definite integrals (the ones with little numbers on the integral sign) to find the area under curves, negative area, and integral properties.

Part of the course(s): ,Test Image Problem ,Calculus

The Trapezoid Rule For Approximating Area Under A Curve

In this video we leave the whole left-vs-right dilemma behind us and just use a formula that's way better than any of that stuff anyway: trapezoidal approximation! And easier to use!

This video appears on the page: Area & Riemann Sums

A Few More Area Approximation Examples

We don't cover a lot of new ground in this one, just get some more practice with a couple of sticky situations, like what to do when one of your rectangles is zero height.

This video appears on the page: Area & Riemann Sums

Left Sum vs Right Sum vs Upper Bound vs Lower Bound

This half-hour video explains pretty much everything you need to know about these problems, then we work a few from left, right and midpoint to sort out all the crazy details of Reimann sums. The goal with these problems is to approximate the area under the curve, but if you've seen this in class, you know this will be obsolete as soon as we hit definite integrals in the next chapter.

This video appears on the page: Area & Riemann Sums

Riemann Sums & Area
Left Sum vs Right Sum vs Upper Bound vs Lower Bound
A Few More Area Approximation Examples
The Trapezoid Rule For Approximating Area Under A Curve

In this chapter we'll approximate area using left-hand sums, right-hand sums, midpoint, upper bounds, lower bounds, and trapezoidal rules. Collectively, these are called "Riemann Sums" or "approximation integration".

Part of the course(s): ,Test Image Problem ,Calculus

Derivatives of Inverse Trig Functions

In this video I show you how to use the inverse trig function derivative formulas. Most classes don't do these, but if you do, you're in luck! Also, I try and show you how you can use any of the more obscure trig derivative formulas that you probably have kicking around the appendix of your book.

This video appears on the page: The Chain Rule