/sci/ - Science & Math

It's literally the product rule backwards

>>9698954
You're an absolute brainlet if you can figure out the proof for integration by parts just by looking at the formula. Your school is also shit

>>9698954
calculus is useless in general. analysis should be taught from the beginning.

I hated Calc 2 but not because of integrals ( I am a beast on those). I hated it because of series and sequences. Professor took points off if you didn't prove you could use a certain test and God help you if you forgot to name it even though you did step by step of it. Outside of deeper integration methods, Calc 2 is the most useless Calc if you are a non-Math major in STEM.

There’s a lot of good applications in Calculus 2. Volume, Surface Area, Center of Mass, Work problems. Those are all pretty important to most people required to take the course.

>>9698978
You are an absolute retard.

>>9699019
And you, I hope, are just trolling or engineer brainlet because if you think that verifying you can use something and don't just mindlessly plug in some shit is meaningless, then you have absolutely no place in science or R&D for that matter.

>deeper integration methods
>Calc 2

C'mon now

>>9699109
meant >>9699109 for OP

>>9699091
Thats calc3

>>9698954
>Also will shit like integration by parts be proven in a later course?
Anon... It's supposed to be obvious. I get it, it can run over your head at first and seem like something complicated, but if you actually put any thought into it and still didn't get it, I'm not sure if university is the right place for you.

I take it that you know the product rule for differentiation and other basic results from calc 1 and calc 2. This is what it boils down to, just taking an integral over both sides and shuffling the terms around. I hope this helps.
[math]D_x(f(x)g(x)) = f(x)g'(x) + f'(x)g(x)[/math]
[math]\int_{a}^{b}D_x(f(x)g(x)) = \int_{a}^{b}f(x)g'(x) + \int_{a}^{b}f'(x)g(x)[/math]
[math]\int_{a}^{b}D_x(f(x)g(x)) - \int_{a}^{b}f(x)g'(x) = \int_{a}^{b}f'(x)g(x)[/math]
[math][f(x)g(x)]_a^{b} - \int_{a}^{b}f(x)g'(x) = \int_{a}^{b}f'(x)g(x)[/math]
[math]\int_{a}^{b}f'(x)g(x) = [f(x)g(x)]_a^{b} - \int_{a}^{b}f(x)g'(x)[/math]

>>9698954
>prove integrations by parts
seriously? how is your professor so shitty that he didnt bother to show the 2 line proof for the formula? how are you so retarded you couldnt figure it out by yourself or simply google it?
[eqn] (uv)' = u'v + uv' [/eqn]
integrate both sides:
[eqn] uv = \int vdu + \int udv [/eqn]
solve:
[eqn] \int udv = uv - \int vdu [/eqn]
I understand asking for a proof/intuiton of LIATE but for the main formula? c'mon my dude

>>9699232
It shouldn't surprise anyone that these OPs are always retards

>>9698954
>Spring semester
>calc 2

>>9698954
>What is the point of calc2? I'll never use it again. I'll use wolfram for integrals.

What's the point of learning addition and multiplication? The cash register will tell you how much change to hand back when you're working at McDonald's or Starbucks.

>>9698954
>engineering
>>>/g/

>>9700095
hmmmm, good point. Why DID i learn that?? useless

>>9700103
>engineering belongs on the computer science board
Pajeet CS will never be engineering despite what your diploma mill uni tells you.

>>9699109
Calc 1 is literally derivatives plus a wee bit of integrals. Calc 2 is literally all integrals plus series and sequence. Pot all schools follow the same semester schedule. Many foreign uni's have calc 1,2,3,4 while in the US Calc 2 is what foreigners would call Calc 2&3 combined.

>>9699138
At your shitty community college, maybe. That's definitely calc 2 material.

>>9701693
foreign unis usually have 2 one-semester classes called mathematical analysis, which in American terms is calculus with elements of analysis, the first one is single variable (including derivatives, integrals, series and sequence), the second one is multivariate.

>>9698954
The fact that calculus takes preeminence in math education is proof the the physics and engineering departments have too much influence over the teaching of math