Areas Between Curves (3 of 3: What about beneath the x-axis?)

[abhimanyuvarma]

Wow....

Mr. Woo, you really explain all these topics in depth and in a very inquisitive/"theoretical" (if that makes sense) way.

I just learned about you a few days ago, when I was searching for a specific concept.

Because of you, I feel as though I might not have to sulk around in a grumpy manner every time I sit to do mathematics.

Thank you for for inspiring me to dive deeper into mathematics (and maybe considering teaching as a job😁), and for sharing a completely different and wonderful perspective on the connection of math and the nature of life.

[XxStuartxX]

A different way to notice this is to imagine your two functions as one: Suppose f(x) is the 'top' and g(x) is the 'bottom' between 2 limit points, and define a new function h(x) = f(x) - g(x). This function is always positive between the limits, because f(x) is always bigger than g(x). Integrating h(x) will give us the area between the curves, and as h(x) is always above the x-axis between the limits, we don't have to worry about splitting the integral up.

Eddie Woo: you are the Wikipedia for the Maths... :-) Thank you very much for your lessons and for sharing your knowledge and expertise.

[mcrettable]

You guys are lucky to have him for a teacher

[alohajackedmiston]

Mahalo Eddie! Bravo Zulu on your Outstanding Instructional Videos!!!! You are truly amazing!

[jeffreyv.]

I imagined subtracting f(x) from g(x) as 'bending' both functions around, until f(x) is at the x-axis. Since f(x) was the bottom function, everything else is therefor going to be above the x-axis. Parts that were below the x-axis would have been raised, parts that were above would have been lowered.

[Supercatzs]

Anyone got the video Mr. Woo was talking about at the end of this lesson?

[johnryder]

5:00 while I never ask myself whose the top Mathematics teacher