When the Teacher Forgets +C After Integrating #shorts @ParthGChannel

Parth G | When the Teacher Forgets +C After Integrating #shorts @ParthGChannel | Uploaded December 2021 | Updated October 2024, 1 week ago.
Our math and physics teachers always remind us to add the constant of integration (+c) whenever we finish an indefinite integral... but sometimes they forget to include it themselves! #shorts

So what do we do in the scenario where our teacher forgets to include this constant? Why we remind them of course! We let them know very firmly and clearly that the integral is indefinite, meaning we have not specified the limits, so we obviously need to add the constant of integration after completing our problem.

Why is the constant even needed at all? Well it's because integration, or at least indefinite integration, does not provide unique solutions. The easiest way to understand this, in my opinion, is to think of the reverse scenario - let's imagine we want to differentiate a function like x^2. We know the derivative of this is 2x. But similarly, the derivative of x^2 + (any constant) is also 2x. Therefore when we integrate 2x our result could be x^2 + any constant. The "solution" we've found is technically representing a family of solutions! And the only way to find the value of our constant c is to define the limits of the integral - this is enough to uniquely identify a solution.

This is one of the first things we learn when studying calculus, and it should be (rightly) drilled into us as early as possible. However teachers are human too, and sometimes they forget to add the constant of integration. In that situation, students should always make sure to remind them :)

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