定积分求详解Byinterpretingadefiniteintegralasanareaunderacurve,evaluate∫(2+√(4x-x^2))dx[0,4]区间Hint:Completethesquareon4x-x^2.Theresultingexpressionshouldleadyoutorecognizeafamiliargeometricalfigure.

Question

定积分求详解By interpreting a definite integral as an area under a curve, evaluate ∫(2+√(4x-x^2)) dx [0,4] 区间 Hint: Complete the square on 4x - x^2. The resulting expression should lead you to recognize a familiar geometrical figure. 请问如何做啊 能给个详解吗

Answer 1

其中后面那个积分就是提示中的The resulting expression should lead you to recognize a familiar geometrical figure.这是圆心在（2，0）半径为2的半圆。定积分的意义就是这个半圆的面积。