Hi, I need help on this problem
Determine all constants a and b such that e^x = b + int_{a, x} e^t dt.
(Thats the integral from a to x)
Thank you
Hello, lds09!
Determine all constants a and b such that:
. . . . . . . . . . . . x
. . e^x . = . b + ∫ e^t dt
. . . . . . . . . . . .a
. . . . . . . . . . . . . . x
We have: .b + e^t ] .= .e^x
. . . . . . . . . . . . . . a
Then: .b + e^x - e^a .= .e^x . . → . . b - e^a .= .0 . . → . . b .= .e^a
Therefore, a can be any real number and b = e^a.