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AP DSC School Assistant Math Model Test 2

Section: Subject Specific

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Question : 64 of 160

Marks: +1, -0

A primitive of | x | , when

x < 0

, is

$\frac{x^{2}}{2}+c$
$-\frac{x^{2}}{2}+c$
x + c
-x + c

Solution:

Concept:

The primitive (antiderivative) of a function

f(x)

is a function

F(x)

such that

F'(x) = f(x)

. The absolute value function

|x|

is defined piecewise: for

x<0

,

|x| = -x

.

Explanation:

For

x < 0

, we replace

|x|

with

-x

and integrate:

\int |x|\,dx = \int (-x)\,dx = -\frac{x^{2}}{2} + c

where

c

is the constant of integration. (For

x\ge 0

, the primitive would be

+\frac{x^{2}}{2}+c

, but the question specifically asks for the case

x<0

.)

Answer:

The correct option is B.

-\frac{x^{2}}{2}+c

.

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