The changes in a function

Question:

The changes in a function $\mathrm{y}$ and the independent variable $\mathrm{x}$ are related as $\frac{d y}{d x}=x^{2}$.

Find $y$ as a function of $x$.

Solution:

It is given that $\frac{d y}{d t}=x^{2}$

We can write $d y=x^{2} d x$

or, $y=\int^{x^{2} d x}=\frac{x^{3}}{3}+c$

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