Topic Content:
- Constant of Integration
If \( \scriptsize y = x^4, \therefore \normalsize \frac{dy}{dx} \scriptsize = 4x^3 \; and \; \int 4x^3 dx = x^4 \)
Also \( \scriptsize y = x^4 \:+ \:2, \therefore \normalsize \frac{dy}{dx} \scriptsize = 4x^3 \; and \; \int 4x^3 dx = x^4 + 2 \)
and \( \scriptsize y = x^4\: -\: 5, \therefore \normalsize \frac{dy}{dx} \scriptsize = 4x^3 \; and \; \int 4x^3 dx = x^4 \: -\: 5 \)
In the three examples, we happen to show the expressions from which the derivative \( \scriptsize 4x^3\)was derived. But any constant term in the original expression becomes zero in the derivative and all trace of it is lost.
So if we do not know the history of the derivative …
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