The value of the integral ∫ 0 π sin 2 x d x is ________.

Put 2 x = t ⇒ 2 d x = d t ⇒ I = 1 2 ∫ 0 2 π sin t d t = ∫ 0 π sin t d t = ∫ 0 π sin t d t = - cos t 0 π = 2

Mathematics - Definite Integration Question with Solution | TestHub

MathematicsDefinite IntegrationProperties of definite integrationMedium2 minPYQ_2021

MathematicsMediumnumerical

The value of the integral $\int_{0}^{π} |\sin 2 x| d x$ is ________.

Answer:

2.00

Solution:

Put $2 x = t \Rightarrow 2 d x = d t$

$\Rightarrow I = \frac{1}{2} \int_{0}^{2 π} |\sin t| d t$

$= \int_{0}^{π} |\sin t| d t$

$= \int_{0}^{π} \sin t d t$

$= {[- \cos t]}_{0}^{π}$

$= 2$

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

⏱ 2mℹ️ Source: PYQ_2021

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