[微積] cosx/(1+sin^2x)

[TVBS2100 (濤歌的節目)]

  π/2   cosx
∫     ------------dx
  0     1+sin^2x


my sol

let sinx = u

then  du = cosxdx
         π
when x= ----  > u = 1
         2

when x= 0     > u = 0
                      _ 1
   1   1           -1  |      -1      -1
>∫  -------du > tan u |  = tan 1 - tan  0
   0  1+u^2           _|
                        0


                          =π/4  - 0

                          =π/4

any problem?

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推 GeeDuTu     :很正確啊