∫ 0 10 ( 10 − x ) 10 + x 10 x 10 d x is equal to

Let I = ∫ 0 10 ( 10 − x ) 10 + x 10 x 10 d x ...(1) I = ∫ 0 10 ( 10 − x ) 10 + x 10 ( 10 − x ) 10 d x ...(2) Adding (1) and (2), we get 2 I = ∫ 0 10 d x ⇒ 2 I = 10 ⇒ I = 5

Mathematics - Definite Integration Question with Solution | TestHub

MathematicsDefinite IntegrationProperties of definite integrationMedium2 minPYQ_2014

MathematicsMediumsingle choice

$\int_{0}^{10} \frac{x ^{10}}{( 10 - x ) ^{10} + x ^{10}} d x$ is equal to

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Solution:

Let $I = \int_{0}^{10} \frac{x ^{10}}{( 10 - x ) ^{10} + x ^{10}} d x$ ...(1) $I = \int_{0}^{10} \frac{( 10 - x ) ^{10}}{( 10 - x ) ^{10} + x ^{10}} d x$ ...(2) Adding (1) and (2), we get $2 I = \int_{0}^{10} d x \Rightarrow 2 I = 10 \Rightarrow I = 5$

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

⏱ 2mℹ️ Source: PYQ_2014

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