Question

数学题，谁能帮我解答下，

求由函数y=sinx、y=cosx、x轴上的线段[0，90°]所围图形绕x轴旋转所成图形的体积？越详细越好，谢谢

Answer 1

求由函数y=sinx,y=cosx,x轴上的线段【0,π/2】所围图形绕X轴旋转所成的旋转体体积？
解：
V=[0，π/4)π∫sin²xdx+[π/4，π/2]π∫cos²xdx
=[0，π/4](π/2)∫(1-cos2x)dx+[π/4，π/2](π/2)∫(1+cosx)dx
=[0，π/4][(π/2)∫dx-(π/4)∫(cos2xd(2x)]+[π/4，π/2][(π/2)∫dx+(π/4)∫cos2xd(2x)]
=[(π/2)x-(π/4)sin2x]︱[0，π/4]+[(π/2)x+(π/4)sin2x]︱[π/4，π/2]
=π²/8-(π/4)+[π²/4-π²/8-π/4]=π²/4-π/2=(π/4)(π-2)