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:
$$\begin{gathered} \frac{dy}{dx}=x^2 \\ \Rightarrow dy=x^{2}dx \end{gathered}$$
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 $y=\frac{x^3}{3}+c$.