Question

The changes in a function y and the independent variable x are related as 
\[\frac{dy}{dx} = x^2\] . Find y as a function of x.

Answer 1

Changes in a function of y and the independent variable x are related as follows:
\[\frac{dy}{dx} = x^2 \]
\[ \Rightarrow dy = x^2 dx\]
Integrating of both sides, we get:
∫dy = ∫x² dx
\[\Rightarrow y = \frac{x^3}{3} + c\]
where c is a constant
∴ y as a function of x is represented by
\[y = \frac{x^3}{3} + c\]