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Question Number 196940 by sonukgindia last updated on 04/Sep/23

	Answered by MM42 last updated on 04/Sep/23

	$s i n 8 x = 8 s i n x c o s x c o s 2 x c o s 4 x$ $\Rightarrow I = 2 \int_{0}^{\frac{π}{4}} c o s x c o s 2 x c o s 4 x d x$ $c o s x c o s 2 x c o s 4 x = \frac{1}{4} (c o s 7 x + c o s 5 x + c o s 3 x + c o s x)$ $\Rightarrow I = \frac{1}{2} (\frac{1}{7} s i n 7 x + \frac{1}{5} s i n 5 x + \frac{1}{3} s i n 3 x + s i n x) ∣_{0}^{\frac{π}{4}}$ $= \frac{\sqrt{2}}{4} (- \frac{1}{7} - \frac{1}{5} + \frac{1}{3} + 1) = \frac{26 \sqrt{2}}{105} ✓$
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