The Fundamental Theorem of Calculus
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The FTC is the rivet that binds derivatives to integrals. It's also a useful tool to cheat your way out of doing some integrals. This is one theorem you want to know.
Want to calculate how fast to throw a nerf ball at your brothers head? The laws of motion are derived here using integration.
The FTC has a doppelganger known as the Second FTC. Check out the not-so-evil twin of the FTC and some examples on how to use it.
No, the antiderivative is not an evil incarnation come to see to the destruction of mathematics. In this video, the antiderivative idea is explained as the inverse of the derivative.
Icebergs and calculus go together like sushi and chopsticks. You can't have one without the other.
Pop open a Dr. Pepper and have Dr. Bob explain these two theorems to you. Take a sip every time he says, "integral".
If a wacky waving inflatable arm flailing tube man captures your attention, this video on the proof of the FTC will do just the same.
Find out how to use antiderivatives to save you from running over a chupacabra. It may be more advantageous to hit it.
With several good examples, you'll feel like a superhero with the power to solve any FTC problem after watching this video. Maybe you'll get laser beam eyes, too.
Applying the Second FTC is a bit like swinging a fly swatter at wasp. Swing it right, and you'll get it. Swing wrong, and you'll get stung. This MIT professor shows you how to use the Second FTC.