Integral with Trig Substitution in UNDER 1 MINUTE! #Shorts

We evaluate the integral of x cubed over the square root of 1 minus x squared using trig substitution. We finish in under a minute making this video an official #Shorts

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[mudasirjan]

i want to make an app that speed runs you through a million integrals. I feel like random vids like this would just on a whole new platform of dopamine for nerds

[GingerMathematician]

Nothing better than integral calculus at speed! 😄

[thegoldlightning]

Dang. Never woulda thought of that. Probably would’ve made a u-sub in the square root.

[benoitdepeault]

doesn't and not cos(theta)? To cancel the cosin, don't you need to show that cos(theta)>=0 to cancel the absolute value? I have been told to precise the domain of theta in order to have a single theta for each x. But I guess drawing the triangle kind of put a restriction on values of theta. Is the drawing enough?

[RainMoneyProductions]

Oh yes I am always in the mood for some trig sub

[slow_bike_show]

I see OneNote for windows 10, I like video. best program for math notes

[yaseenelhosseiny]

The hardest part for me was integrating sin^3(theta) dtheta

[the.lemon.linguist]

how did you get d(theta) to equal that?

did you find the derivative of theta and then just rearrange the equation algebraically?

[colloidalsilver]

Why was I assuming you’d use U-sub? Excuse my ignorance but what made you use a trig ID?

[elkincampos]

The best. Let u=√(1-x^2) because du=-x/(√(1-x^2)) and x^2=u^2-1.

[elietheprof]

Ya but wouldn't that only work for -1 <= x <= 1 ? Sines and cosines don't go beyond that...