If ∫ 0 π /2 sin 8 x cos 4 x d x = 2048 kπ then the value of k must be

∫ 0 π /2 sin 8 x cos 4 x d x = 12 ⋅ 10 ⋅ 8 ⋅ 6 ⋅ 4 ⋅ 2 ( 7 ⋅ 5 ⋅ 3 ⋅ 1 ) ( 3 ⋅ 1 ) ⋅ 2 π ( by Wallis’ formula ) = 2048 7 π ⇒ k = 7

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MathematicsDefinite IntegrationWalli's FormulaEasy2 minQB

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If $\int_{0}^{π /2} sin^{8} x cos^{4} x d x = \frac{kπ}{2048}$ then the value of $k$ must be

Answer:

Solution:

$\int_{0}^{π /2} sin^{8} x cos^{4} x d x = \frac{( 7 \cdot 5 \cdot 3 \cdot 1 ) ( 3 \cdot 1 )}{12 \cdot 10 \cdot 8 \cdot 6 \cdot 4 \cdot 2} \cdot \frac{π}{2}$

$(by Wallis’ formula) = \frac{7 π}{2048} \Rightarrow k = 7$

Stream:JEESubject:MathematicsTopic:Definite IntegrationSubtopic:Walli's Formula

⏱ 2mℹ️ Source: QB

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