Question

Converges or Diverges?

Answer 1

\[\int\limits_{1}^{\infty}e ^{-x}sinxdx\]

Answer 2

integrate by parts, what do you get?

Answer 3

make u=sinx, correct? and then integrate by parts

Answer 4

makes no difference which you make u and which you make dv in this case, but yeah

Answer 5

@TuringTest I get a 0 :/ so that means that it should diverge

Answer 6

what was the expression you got after integrating but before evaluating?

Answer 7

evaluating at infinity gives zero, but what about evaluation at 1 ?

Answer 8

ended up with -sinx*e^-x - sinxe^-x

Answer 9

yeah so evaluate the integral and you get 0-(something) which is not divergent

Answer 10

0-(-0.0128)

Answer 11

yeah sounds right... the point is, it ain't infinity, so convergent

Answer 12

yes :) thanks a lot @TuringTest