Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Definite Integration

Question:

\(\int_{0}^{3}[x]dx=\) (where \([\cdot]\) denotes the greatest integer function).

Options:

2

3

1

0

Correct Answer:

3

Explanation:

\(\int_{0}^{3}[x]dx=\int_{0}^{1}[dx]dx+\int_{1}^{2}[x]dx+\int_{2}^{3}[x]dx\)

$=\int_{0}^{1}0dx+\int_{1}^{2}1dx+\int_{2}^{3}2dx$

$=1×(2-1)+2×(3-2)$

$=3$