f'x=sin(x-1)^2 f0=0 求∫ (0,1) f(x)dx

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f'x=sin(x-1)^2 f0=0 求∫ (0,1) f(x)dx

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)

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