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Integration and Differentiation of a Trigonometric Function

Given f(x)=sin⁡x+cos⁡xf(x)=\sin x+\cos xf(x)=sinx+cosx, find its derivative, horizontal tangents on [0,π][0,\pi][0,π], area under the curve from 000 to π2\frac{\pi}{2}2π​, and volume of revolution.

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