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Concepts Of Physics MCQ Edition [Volume 1]

Exam: Concepts Of Physics MCQ Edition [Volume 1]
Subject: Physics
Chapter: Physics and Mathematics

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Physics and Mathematics

The relationship between the changes in a function y and an...

The relationship between the changes in a function

y

and an independent variable

x

is given by

\dfrac{dy}{dx} = x^2

. Determine

y

as a function of

x

.

Options

A $y = \dfrac{x^2}{2} + C$
B $y = \dfrac{x^3}{3} + C$
C $y = \dfrac{x^3}{3}$
D $y = 2x + C$

Correct answer

B. $y = \dfrac{x^3}{3} + C$

Step-by-step solution

Given

\dfrac{dy}{dx} = x^2

Integrating both sides with respect to

x

:

\int dy = \int x^2 dx

y = \dfrac{x^3}{3} + C

where

C

is the constant of integration.

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