I Is It Possible? Solving Calculus Questions with Ease

[NODARman]

TL;DR Summary

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Hi, just wondering if that's possible in calculus.
(See the attachment)

 

[topsquark]

TL;DR Summary: .

Hi, just wondering if that's possible in calculus.
(See the attachment)

What you wrote was essentially correct. But...

In reality? No. The derivative notation $\dfrac{d \theta }{dt}$ is not actually a fraction so you cannot cancel the dt's.

However, in practice you can "cancel" the dt's. It's a similar effect to the chain rule: $\dfrac{d \theta }{dx} = \dfrac{d \theta }{dt} \cdot \dfrac{dt}{dx}$. Again, there is no real cancellation, but it appears that way.

Mathematicians in the 1800s spent a great deal of time showing how you can treat a differential element as a fraction. Most of the time you can get away with it.

-Dan

 

[PeroK]

Technically the bounds on the integral need to change to $\int_{t(0)}^{t(2\pi)}$ if you are integrating wrt $t$.