the best series you'll ever watch

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okay guys i said tomorrow we'll touch on integrals, the second half of calculus; who wants to know how to find the area under curves?

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to find the area under a curve in the x^2+mx+b format, we first need to find what is called an anti-derivative; for simple x^2+mx+b curves, finding the anti derivative is simple. First, throw out the constant, 'b', you don't need it. Now, what you're going to do, for each piece of the x^2+mx function, you simply need to add 1 to its exponent then divide that piece of the equation by whatever number the exponent now is.
the antiderivative of x^n will be (x^(n+1))/(n+1)
so, for the curve y=x^2, the antiderivative will be (x^3)/3.
To find the area underneath that curve between the lines x=1 and x=3, simply plug both of those x values into the anti-derivative, and subtract.
So, for the area between x=1 and x=3 under the curve y=x^2, we plug 3 into the antiderivative (which is (x^3)/3) getting 9, then plug 1 into the antiderivative getting 1/3.
9 - 1/3rd is 8 and 2/3rds, so the area is 8.6666666666 squared

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you now know integrals, the second half of calculus

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the reason you dont need the constant is because you can find the remaining area under the curve using your standard length*width rule for finding the area of rectangles

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of course it does get more complicated, like finding the area under sin waves and shit, but if you need to know that then you should probably go to school for it

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lisa youre a maniac on the floooooor

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oh god im drunk, please don't start hitting on lisa again, please