For any integer n, the value of ∫_(-π)^π e^(cos^2 x) sin^3 (2n+1)x dx is
(a) -1 (b) 0 (c) 1 (d) 2
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CBSE Class 12 Sample Paper for 2024 Boards
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CBSE Class 12 Sample Paper for 2024 Boards
Last updated at Aug. 14, 2023 by Teachoo
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This is of the form β«_(βπ)^πβπ(π₯)ππ₯ where π(π)=π^(γπππγ^π π) γπ¬ππγ^π (ππ+π)π And, π(βπ₯)=π^γπππγ^πβ‘(βπ) sin^3β‘γ[(2π+1)γ (βπ)] Since cos (-x) = cos x π(βπ₯)=π^(γπππ γ^2β‘π₯) γsππγ^3β‘[β(2π+1)π₯] Since sin (-x) = βsin x π(βπ)=γβπγ^(γπππγ^πβ‘π) γπππγ^πβ‘(ππ+π)π Thus, π(βπ₯)=βπ(π₯) β΄ β«130_(βπ )^π ββ π^(γπππγ^π π) γπππγ^π (ππ+π)ππ π=π So, the correct answer is (b)