સંકલન int_{pi / 6}^{pi / 2} left( frac{1+sin | vedclass

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(D) ધારો કે $I = \int_{\pi / 6}^{\pi / 2} \left( \frac{1+\sin 2x+\cos 2x}{\sin x+\cos x} \right) dx$ નિત્યસમ $\sin 2x = 2\sin x \cos x$ અને $\cos 2x =

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$1$

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(D) ધારો કે $I = \int_{\pi / 6}^{\pi / 2} \left( \frac{1+\sin 2x+\cos 2x}{\sin x+\cos x} ight) dx$ નિત્યસમ $\sin 2x = 2\sin x \cos x$ અને $\cos 2x = 2\cos^2 x - 1$ નો ઉપયોગ કરતા: $I = \int_{\pi / 6}^{\pi / 2} \left( \frac{1 + 2\sin x \cos x + 2\cos^2 x - 1}{\sin x + \cos x} ight) dx$ $I = \int_{\pi / 6}^{\pi / 2} \left( \frac{2\cos x(\sin x + \cos x)}{\sin x + \cos x} ight) dx$ $I = \int_{\pi / 6}^{\pi / 2} 2\cos x dx$ $I = 2[\sin x]_{\pi / 6}^{\pi / 2}$ $I = 2\left( \sin \frac{\pi}{2} - \sin \frac{\pi}{6} ight)$ $I = 2\left( 1 - \frac{1}{2} ight) = 2 	imes \frac{1}{2} = 1$

સંકલન $\int_{\pi / 6}^{\pi / 2} \left( \frac{1+\sin 2x+\cos 2x}{\sin x+\cos x} \right) dx$ ની કિંમત કેટલી થાય?

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