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The integral is equal to:
MATHEMATICS · Single correct · CBSE · Mathematics · Integrals · Integrals
Problem The integral ∫ π / 4 π / 2 ( 2 csc x ) 17 d x \int_{\pi/4}^{\pi/2}(2\csc x)^{17}\,dx ∫ π /4 π /2 ( 2 csc x ) 17 d x is equal to:
(1) ∫ 0 log ( 1 + 2 ) 2 ( e u + e − u ) 16 d u \int_{0}^{\log(1+\sqrt{2})}2(e^u+e^{-u})^{16}\,du ∫ 0 l o g ( 1 + 2 ) 2 ( e u + e − u ) 16 d u
(2) ∫ 0 log ( 1 + 2 ) ( e u + e − u ) 17 d u \int_{0}^{\log(1+\sqrt{2})}(e^u+e^{-u})^{17}\,du ∫ 0 l o g ( 1 + 2 ) ( e u + e − u ) 17 d u
(3) ∫ 0 log ( 1 + 2 ) ( e u − e − u ) 17 d u \int_{0}^{\log(1+\sqrt{2})}(e^u-e^{-u})^{17}\,du ∫ 0 l o g ( 1 + 2 ) ( e u − e − u ) 17 d u
(4) ∫ 0 log ( 1 + 2 ) 2 ( e u − e − u ) 16 d u \int_{0}^{\log(1+\sqrt{2})}2(e^u-e^{-u})^{16}\,du ∫ 0 l o g ( 1 + 2 ) 2 ( e u − e − u ) 16 d u
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