Q56 / 90 · JEE Main 2021 (17 Mar Shift 1) · Mathematics

If $[\cdot]$ represents the greatest integer function, then the value of $|\int_{0}^{\sqrt{\frac{π}{2}}} [[x^{2}] - \cos x] d x|$ is ___________.

Correct answer: 1

Solution

$I = \int_{0}^{\sqrt{π / 2}} ([x^{2}] + [- \cos x]) d x$

$= \int_{0}^{1} 0 d x + \int_{1}^{\sqrt{π / 2}} d x + \int_{0}^{\sqrt{π / 2}} (- 1) d x$

$= \sqrt{\frac{π}{2}} - 1 - \sqrt{\frac{π}{2}} = - 1$

$\Rightarrow |I| = 1$

Hence, the correct answer is 1.