Intro to Integration & Anti-Derivatives
The Power Rule (no U-Substitution)
So there was a power rule in derivatives with the same name, but I doubt you'll get them confused because they're exact opposites. Uh-oh, that's confusing? Don't worry, this is everyone's favorite integral formula. In this video we'll integrate some easy examples, but also show how some algebra can make harder ones doable as well.
Why The Heck Do We Need +C?
"C", otherwise known as the constant of integration, can cost you a lot of points if you forget it because it's in every freaking problem. But what does it mean? Where did it come from and where is it going? And how do I solve those pesky "initial value" problems?
Integrating Roots Radicals & Fractions (no U-Sub)
In previous chapters, we took the derivatives of roots and radicals with the power rule by turning them into fractional exponents. Not surprisingly, we're going to take the same approach with integration. Because it works. If you need to do these with u-substitution, that's in a later chapter.
Trig Function Integrals (without U-Substitution)
As you've noticed by now, integral formulas are just the same as the derivative formulas, except they're backwards. Nowhere is that more confusing than with trig functions, which are confusing and complicated to begin with. But don't worry, I work examples so messy that you'll be relieved when you see the relatively straightforward stuff your teacher puts on the test.
Log & Exponential Integrals (without U-Substitution)
There's not a lot you can do with exponentials and logs without U-substitution, but we'll give it a try! Basically just warming up your algebra skills for the craziness waiting for you later in Calculus.