[微積] 高微一題

[tsaihohan (有人想一起下圍棋嗎)]

        Let D be the rectangle in RxR given by

        D={(x,t)│a≦x≦b, c≦t≦d}. Let f and its partial

        derivative f_t be continuous functions defined on

        D, and F be a function on [c,d] given by

              b
        F(t)=∫f(x,t)dx. Prove that F has a derivative on
              a
                         b
        [c,d] and F'(t)=∫f_t(x,t)dx.
                         a

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