Question

I'm asked to calculate the integral from x to infinity of (e^-y)dy . Please refresh on how USubstition works

Answer 1

\[\int\limits_{x}^{\infty} e^{-y}dx\]

Answer 2

basically you use u to make the equation look easier to solve, so for instance u=-y and du=-dy. Which would make this equation -e^u du, which intergrates to -e^u, or the integral will be -(e)^(-y)

Answer 3

oh different problem, dx not dy, hmmm

Answer 4

do you have a function for y

Answer 5

that should be dy

Answer 6

oh ok then what I said earlier should be correct.

Answer 7

how do u know what to pick for u again?

Answer 8

basically you need to pick a u which makes the equation look like one you know how to integrate.

Answer 9

oh i remember that ! gotcha thanks man

Answer 10

ultimately though it mostly takes practice, no problem

Answer 11

you could let
u= -y
and du = - dy or dy= -du
and adjust the limits: when y is x u=-x and when y= infinity , u = -infinity

but is hardly worth it. rather, notice the derivative of e^-y = e^-y -dy
if you put in a -1 *dy (and a -1 out front to compensate)
you can integrate directly.

Answer 12

this looks like improper integrals