Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Definite Integration

Question:

$\int\limits_0^4\{\sqrt{x}\}$ is equal to, where x denotes the fraction part of x.

Options:

$\frac{2}{3}$

$\frac{16}{3}$

$\frac{5}{3}$

$\frac{7}{3}$

Correct Answer:

$\frac{7}{3}$

Explanation:

We have,

$\int\limits_0^4\{\sqrt{x}\} d x=\int\limits_0^1 \sqrt{x} d x+\int\limits_1^4(\sqrt{x}-1) d x=\frac{2}{3}+\frac{2}{3}(8-1)-3=\frac{7}{3}$