作业帮微积分~第十三
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微积分~第十三
Solve:Find the solution of y=sinx and y=1/2 in the domain [0, π]:x=π/6, 5π/6See the figure below:
The area bounded by the curve y=sinx and the line y=1/2 in the domain [0, π] is∫ [π/6..5π/6] (sinx-1/2) dx = (-cosx - x/2) | [π/6..5π/6]=√3/2 - 5π/6/2 + π/6/2 + √3/2=√3 - π/3
The area bounded by the curve y=sinx and the line y=1/2 in the domain [0, π] is∫ [π/6..5π/6] (sinx-1/2) dx = (-cosx - x/2) | [π/6..5π/6]=√3/2 - 5π/6/2 + π/6/2 + √3/2=√3 - π/3