The solution for x of the equation ∫ 2 x t t 2 − 1 d t = 2 π is

∫ 2 x t t 2 − 1 d t = 2 π [ sec − 1 t ] 2 x = 2 π sec − 1 x − 4 π = 2 π sec − 1 x = 4 3 π x = − 2 .

Mathematics - Definite Integration Question with Solution | TestHub

MathematicsDefinite IntegrationProperties of definite integrationMedium2 minPYQ_2007

MathematicsMediumsingle choice

The solution for $x$ of the equation $\int_{2}^{x} \frac{d t}{t t ^{2} - 1} = \frac{π}{2}$ is

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Solution:

$\int_{2}^{x} \frac{d t}{t t ^{2} - 1} = \frac{π}{2}$ $[sec^{- 1} t]_{2}^{x} = \frac{π}{2}$ $sec^{- 1} x - \frac{π}{4} = \frac{π}{2}$ $sec^{- 1} x = \frac{3 π}{4}$ $x = - 2$ .

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

⏱ 2mℹ️ Source: PYQ_2007

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