Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Indefinite Integration

Question:
If \([x]\) denotes the greatest integer function of \(x\) then \(\int_{a}^{b}[x]dx+\int_{b}^{a}[-x]dx=\)
Options:
\(2(b-a)\)
\(2(a-b)\)
\(a-b\)
\(0\)
Correct Answer:
\(2(b-a)\)
Explanation:
\(\begin{aligned}\int_{a}^{b}[x]dx+\int_{b}^{a}[-x]dx&=[x]_{a}^{b}+[-x]_{b}^{a}\\ &=2(b-a)\end{aligned}\)