Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Applications of Derivatives

Question:

$\int_0^{1.5}[x]dx$, where [x] denotes the greatest integer function $≤x$, is equal to :

Options:

$\frac{1}{4}$

$\frac{1}{2}$

1

0

Correct Answer:

$\frac{1}{2}$

Explanation:

Graph of greatest integer function

$\int_0^{1.5}[x]dx$ → area under curve

from x = 0 to x = 1

area = 0

form 1 to 1.5

area = 0.5 × 1 = 0.5

so, total area = 0.5 sq. units