The value of the integral ∫ 0 2 π [ 2 sin x ] d x is ([.] denotes the greatest integer function)

Let I = ∫ 0 2 π [ 2 sin x ] d x . = ∫ 0 π /6 0 d x + ∫ π /6 5 π /6 1 d x + ∫ 5 π /6 π 0 d x + ∫ π 7 π /6 ( − 1 ) d x + ∫ 7 π /6 11 π /6 ( − 2 ) d x + ∫ 11 π /6 2 π ( − 1 ) d x

Mathematics - Definite Integration Question with Solution | TestHub

MathematicsDefinite IntegrationProperties of definite integrationEasy2 min

MathematicsEasysingle choice

The value of the integral $\int_{0}^{2 π} [2 sin x] d x$ is ([.] denotes the greatest integer function)

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Solution:

Let $I = \int_{0}^{2 π} [2 sin x] d x$ .

$= \int_{0}^{π /6} 0 d x + \int_{π /6}^{5 π /6} 1 d x + \int_{5 π /6}^{π} 0 d x + \int_{π}^{7 π /6} (- 1) d x + \int_{7 π /6}^{11 π /6} (- 2) d x + \int_{11 π /6}^{2 π} (- 1) d x$

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

⏱ 2m

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