Integral of The Absolute Value of Sine from 0 to 3pi/2

Integral of The Absolute Value of Sine from 0 to 3pi/2

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[smashandburnff]

This channel makes calculus 1 and 2 a lot more intuitive.

[cepheusclips]

This was super cool, thanks for submitting this to the internet highway.

[thiagovieira]

with symmetry ... integral from 0 to 3pi/2 of |sin(x)| dx = 3*integral from 0 to pi/2 of sin(x) dx = 3*( -cos(pi/2) + cos(0) ) = 3*1=3
and
with symmetry u can deduze one formula :

integral from mpi/2 to npi/2 |sin(x)| dx =n-m with n and m integers
I won't prove it algebraically here because I would have to keep dividing into cases of n and m. It can be seen only by the graph and understanding that because of the module, you will only add positive portions

[BlackHermit]

The beginning of (-sinx) is the ray. Forget not the humble beginnings from which Rachmaninoni issued forth the radiating (sinx).

[hussainfawzer]

this could be done in head, without writing down anything. too easy.

people who are learning calculus, please know that calculus is too easy. if you are good in algebra, calculus is a piece of cake. Most of the people I know are freaked out by calculus because it involves lot of new symbols, when you start. People don't let that thing fool you. Always say this mantra to yourself, Calculus is easy.

An Advice I like to follow is,
when you study calculus, try to understand very thing but remember how you derive the formulas like (power formula, quotient formula, etc). Once you study the proofs, try to redo the proof often and make sure you understood the proof and you could derive it when ever you want it.( just don't memorize the results) and another thing if you're studying calculus for the first time please don't look at the delta epsilon definition of limit. I mean you can look at it and get the idea, why it is the definition of a Limit but don't expect to prove every limit with that definition ( I mean you can do it but sometimes you may get intimidated by those proofs).