Question

Integrate

Answer 1

\[\int\limits _{0}^{\infty} \lfloor x \rfloor e^{-x} dx\]

Answer 2

I am getting 1/(e-1)

Answer 3

absolute value of x right?

Answer 4

Right.

Answer 5

I get 1, but i'll check again

Answer 6

Hmm can't do the integral but the aproximation I do get to 1.

Answer 7

that initially seemed like floor value of x..... :P

Answer 8

trid partial integration?

Answer 9

i also get 1.

Answer 10

Yeah one more which i was doing was Integral (x^2/x^2+1) and i got x- arctanx by trig sub.

Answer 11

thats correct....and can be done without substitution...

Answer 12

if u can use this integral as standard
int 1/(1+x^2) dx = arctan x +c

Answer 13

btw forget what I said about partial integration... looks like geting no where.

Answer 14

after IBP, i get the integral of:
\[\large [-e^{-x}(x+1)]^\infty_0\]

i made the leap that -e^(-x) tends to zero much faster than x+1 tends to infinity as x goes to infinity, but can't give a real justification right now

Answer 15

Looks just about right Mathmuse. Seems like I made a bad choise when I did IBP.

Answer 16

looks the same, wots 'sign(x)'?

Answer 17

The sign function?