f'x=sin(x-1)^2 f0=0 求∫ (0,1) f(x)dx

来源：学生作业帮编辑：灵鹊做题网作业帮分类：数学作业时间：2024/05/14 15:03:32

f(x)=∫ (0,x) sin(y-1)^2dy
∫ (0,1) f(x)dx=∫ (0,1)dx∫ (0,x) sin(y-1)^2dy
=∫ (0,1)dy∫ (y,1) sin(y-1)^2dx
=∫ (0,1)(1-y)sin(y-1)^2dy
=(1/2)cos(y-1)^2|(0,1)
=(1/2)(1-cos1)
再问：第三个等号开始不太懂
再答： =∫ (0,1)(1-y)sin(y-1)^2dy =-(1/2)∫ (0,1)sin(y-1)^2d(y-1)^2 (相当于sinxdx) =(1/2)cos(y-1)^2|(0,1) =(1/2)(1-cos1)

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