∫ 0 π 2 c o s θ . s i n 3 θ d θ = …

Question

∫ 0 π 2 c o s θ . s i n 3 θ d θ = …, - 20 21, - 8 21, 20 21, 8 21

MARKS App · Accepted Answer

Let l = ∫ 0 π 2 c o s θ . s i n 3 θ d θ = ∫ 0 π 2 c o s θ . s i n θ 1 - c o s 2 θ d θ Put c o s θ = t ⇒ - s i n θ d θ = d t ⇒ s i n θ d θ = - d t If θ = 0 , t = 1 a n d θ = π 2 , t = 0 ∴ l = ∫ 1 0 t 1 - t 2 - d t = ∫ 0 1 t 1 / 2 - t 5 / 2 d t = t 3 / 2 3 2 - t 7 / 2 7 2 = 2 3 t 3 / 2 - 2 7 t 7 / 2 0 1 = 2 3 - 2 7 - 0 - 0 = 14 - 6 21 = 8 21

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