Question

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Answer 1

\[\int\limits_{\alpha}^{\beta}\sqrt{t^3+1}dt\]find partial derivative respect to alpha, beta

Answer 2

this is differentiation under integral sign..
but, hold it,
are alpha and beta functions of some "u" or just constants?

Answer 3

the original one is F(alpha,beta) = integral ...You say. are they functions or constants? I don't know

Answer 4

no, they are functions

Answer 5

\[
{\partial\over\partial u}\int_\alpha^\beta f(t)dt=f(\beta){\partial\beta\over\partial u}-f(\alpha){\partial\alpha\over\partial u}
\]

Answer 6

I think the safest way is take integral first to get a "new" function respect to alpha and beta separately . then partial derivative. by that way, it's no longer depend on function or constant. is it right?

Answer 7

i took alpha and beta as functions of "u".
so, instead, use alpha and beta instead of "u"

Answer 8

(a) would be "-sqrt(a^3+1)"
(b) would be "sqrt(b^3+1)"

Answer 9

bingo. i got it

Answer 10

too, my bad computer !! jump every where

Answer 11

thanks elect

Answer 12

rokid, sorry