Question

Zarkon !!! What am I supposed to be doing here?? "Consider y(x)=(x-1) integral from 0 to x, t*f(t)dt + integral from x to 1 , (t-1) * f(t) dt.....use Leibniz' rule (twice) to calculate y"(x)" ???

Answer 1

integrate them separately then add their limits .u must first differentiate y'' then sub it to the integral

Answer 2

ok.....and how would I go about even starting that???

Answer 3

t and f(t ) use by parts

Answer 4

diffrentiate f(t) and integrate t

Answer 5

so how would the first line look??

Answer 6

first y'' is zero then it will affect the fist integral by making it to be zero .hence you will have 0 + \[\int\limits_{x}^{1}\](tf(t)-f(t)) dt then use by parts for f(t)t

Answer 7

why is y" = 0

Answer 8

differentiate it twice

Answer 9

that's my question, I guess...HOW do I differentiate it, even once? I'm totally lost on what the prof was doing here....

Answer 10

separate then differentiate twice

Answer 11

sorry i'm going to the class i'll finish it .but it is interesting

Answer 12

ok, thanks!