∫−3/210 {2x}dx where {.} denotes the fractional part of x, is equal to

A
$\frac{1}{2}$
B
$\frac{13}{2}$
C
$\frac{23}{2}$
D
$\frac{23}{4}$

Solution:

$f (x) = {2 x}$ is a periodic function with period $\frac{1}{2}$

Let

$\begin{array}{l} I = \int_{- 3 / 2}^{10} {2 x} dx = \int_{- 3 (1 / 2)}^{20 (1 / 2)} {2 x} dx \\ = 23 \int_{0}^{1 / 2} 2 xdx \\ [as {2 x} = 2 x - [2 x] and when \in [0, \frac{1}{2}), [2 x] = 0] \\ = 23 {[x^{2}]}_{0}^{1 / 2} = \frac{23}{4} \end{array}$

Related content

Test your English Vocabulary

CUET Exam Dates 2024 – Application Form, Fees, Eligibility

CBSE Class 12 IP Answer Key 2024,Informatics Practices Paper Solution For SET 1, 2, 3, 4

CUET UG Cut Off 2024, Category, Universities and Colleges Wise Expected Cut Off

Modal Verbs

Helping Verbs

Letter To Your Friend About Your School Trip

Action Verbs

CUET 2024 – List of Colleges and Participating Universities Accepting CUET Exam Score

SRMJEEE Online Test Series – Practice Papers