Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# The Changes in a Function Y and the Independent Variable X Are Related as D Y D X = X 2 . Find Y as a Function of X. - Physics

Sum

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.

#### Solution

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

Concept: What is Physics?
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#### APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 1
Chapter 2 Physics and Mathematics
Exercise | Q 29 | Page 30
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