d/da∫sinx^2dx,∫从a到b

Question

d/da∫sinx^2dx ,∫从a到b

Answer 1

请记住公式:d( ∫（上限是h(x) 下限是g(x)）f(x)dx )/dt = f（h(x)）h'(x)-f(g(x))g'(x)
d/da∫sinx^2dx ,∫从a到b
=sinb^2b'-sina^2a'这里,是对a求导.
=-sina^2
方法2
设∫sinx^2dx =f(x)
则df(x)/dx=sinx^2
则则∫sinx^2dx ,∫从a到b
=f(b)-f(a)
d∫sinx^2dx /da,∫从a到b
=d{(f(b)}/da-d{f(a)}/da
=0-d(f(a))/da
因为df(x)/dx=sinx^2
所认,
d∫sinx^2dx /da,∫从a到b
=-sina^2