Question

Evaulate the integral by parts \[\int\limits_{0}^{1}y/e ^{2y} dy\]

Answer 1

\[\int_0^1 \frac{y}{e^{2y} }dy\] ?

Answer 2

yah that

Answer 3

im not getting the correct answer

Answer 4

the answer is 1/4 - (3/4)(e^-2)

Answer 5

lets try this again
\[\int ye^{-2y}dy\]
\[\frac{y e^{-2y}}{-2} - \int\frac{e^{-2y}}{-2}\]
\[ - \frac{ye^{-2y}}{2} - \frac{e^{-2y}}{4}\]

Answer 6

so now when we put the limits

Answer 7

i did things wrong in my first attempt not this one atleast thats what i think lol

\[-\frac{e^{-2}}{2} - \frac{e^{-2}}{4} + \frac{1}{4}\]

Answer 8

\[\frac{1}{4} - \frac{-3e^{-2}}{4}\]

Answer 9

ok i kinda get the steps now

Answer 10

good : )

Answer 11

gotta change to e^-2y

Answer 12

yeah that makes it easy to think and perform in my first attempt i didn't do it and had trouble

Answer 13

yeah thats what i didnt do