Definite Integration

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• \(\int_0^{\pi/2}\frac{\sin x}{\sin x+\cos x}\,dx=\) Answer: C. π/4 Using x→fracπ2-x , I=∫cos x/sin x+cos xdx ; adding, 2I=fracπ2 . Definite Integration 1 answer
• \(\int_0^1 x(1-x)^5\,dx=\) Answer: B. 1/42 Using x→1-x : ∫₀¹(1-x)x⁵dx=1/6-1/7=frac142 . Definite Integration 1 answer