The changes in a function y and the independent variable x are related as d y-d x-x2- Find y as a function of x

Change in a function of y and the independent variable x are related as, dy/dx = x^2 ⇒ dy = x^2 dx Taking integration of both sides, we get ∫ dy = ∫x^2 dx ...

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Standard XII

Mathematics

Average Rate of Change

The changes i...

Question

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

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Solution

Change in a function of y and the independent variable x are related as,

$\frac{d y}{d x} = x^{2}$

$\Rightarrow d y = x^{2} d x$

Taking integration of both sides, we get
$\int d y = \int x^{2} d x$

$\Rightarrow y = \frac{x^{3}}{3} + c$

$∴$ y as a function of x is represented by,

$y = \frac{x^{3}}{3} + c$

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The changes in a function y and the independent variable x are related as dydx=x2, Find y as a function of x.

Change in a function of y and the independent variable x are related as, dydx=x2 ⇒ dy =x2 dx Taking integration of both sides, we get ∫dy=∫x2 dx ⇒ y=x33+c ∴ y as a function of x is represented by, y=x33+c

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