Integral of sin(3x) || Calculus 1 Practice Problems

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We integrate the sine of 3x. We do this using u substitution. I hope this helps someone learning calculus.
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You know a mathematician when he uses chalkboard or paper or a physicist (we’re fed up of all the apps) when he needs a huge board to write on. For the engineers they only want their iPads/tabs for some reason.

dean

the answer is obtained by u-substitution but I simplify it by calling it the "anti-chain rule".

Since derivative of `sin(ax)` is `a*cos(ax)` via the chain rule: `∂f/∂x = ∂f/∂u * ∂u/∂x` OR `f'(u) * g'(x) where u=g(x)`.
the anti-chain rule works in reverse like: `[∫f(u)∂u / g'(x)], where u=g(x)` OR `∫`f(u)∂u / [∂u/∂x]`.

kevinyonan

It amazes me how many folks I've meet that can bteeze through IBP's, some could even rip diffie Q's apart and solve. But substitution flubs these people up for some reason!?!

erthx

When you treat the derivative as a fraction there, why are you allowed to do that? i.e du = 3dx

I see this sort of "fast and loose" stuff in physics. It feels like something you could accidently misuse and end up with the wrong answer.

CkwopPabalo

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