Mathematics - Definite Integration Question with Solution | TestHub

MathematicsDefinite IntegrationProperties of definite integrationMedium2 minPYQ_2021

MathematicsMediumnumerical

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

Answer:

1.00

Solution:

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

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

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

$\Rightarrow |I| = 1$

Stream:JEESubject:MathematicsTopic:Definite IntegrationSubtopic:Properties of definite integration

⏱ 2mℹ️ Source: PYQ_2021

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