Parametric vs. Cartesian (vid#5): Area

How to find area under parametric curve,

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blackpenredpen | 曹老師

[Pinjesz]

Am i wrong or both integrals equal 36, not 100/3?

[MarioFanGamer]

The answer for both integrals is 36. Both of them can be done in the head: The first one is easy to integrate (a constant plus an easy square root) on its own but but also has got squares in the radicals for these values and the second one can be solved with the binomial formula (a + b)(a - b) (though it's more (a + b)(2a - 2b) but that's just 2(a + b)(a - b)) which again, makes the integral easy to integrate.

[Sarah-pqdm]

[2/3t^3 - 2t] 4, 1 then you get 36 for both

[Boycicle]

Studying for my final right now, and this was really helpful

[aarn]

Wait, what happens if we go from, say, t=0 to t=2. Since we know this equation overlaps on that range, what would the method calculate? Would it just add the "areas" together?

[ibrt]

Wait a minute...in Cartesian form you got to integrate a horrible square root function, but in parametric form you got to integrate a nice polynomial. Could this technique be used to solve ugly integrals, by first converting them to parametric form?

[Flanlaina]

Don’t put down “You do it” and “still a secret” on the test!

[MrHK]

Yes 36 is right answer but I understand that sometimes all does mistakes so no problem

[andersjohnson]

69th like! 69 is the last Integer factorial under a google

[sergioh]

Using those same x(t) and y(t), find the area using vector analysis 😀

[rpilipinas]

Wish he'd get a lapel mic. He could be more expressive with a free hand. 👍

[simulacrumx]

Whenever you say parameter I hear perimeter.

[ThePharphis]

I love the channel but the kid sounds are really jarring lol