Test Index

UPSC NDA I 2024 Mathematics Paper

Show Para Hide Para

Consider the following for the next two (02) items that follow :

Let

f(x)=|x-1|, g(x)=[x]

and

h(x)=f(x) g(x)

where [.] is greatest integer function.

© examsnet.com

Question : 93 of 120

Marks: +1, -0

What is

\int\limits_{-1}^{0} h(x) dx

$-\;\frac{3}{2}$
-1
0
$\;\frac{1}{2}$

Solution:

\;\int\limits_{-1}^{0} h(x) dx\;=\int\limits_{-1}^{0} f(x) \cdot g(x) \cdot dx

\;\int\limits_{-1}^{0|x-1|} \cdot [x] dx

\;=\int\limits_{-1}^{0} (1-x) \cdot (-1) dx

\;=\int\limits_{-1}^{0} (x-1) dx

\;=\left[ \frac{x^2}{2} - x \right]_{-1}^{0} = \left[ 0 - \left( \frac{1}{2} + 1 \right) \right]

\;=-\;\frac{3}{2}

© examsnet.com

Go to Question:

Prev Question

Next Question