Question

i just need to see the steps

Evaluate \(\Large \int_{-\infty}^{0} xe^x dx\)

Answer 1

Try integration by parts

Answer 2

u=x dv/dx=e^x
du=dx v=e^x

Answer 3

xe^x + e^x?

Answer 4

xe^x - e^x

Answer 5

the formula is \[uv-\int\limits_{}^{} v~du\]

Answer 6

\[\int\limits_{n}^{0}xe ^{x}dx\] is (x-1)e^x using integration by parts
applying the limits we get the answer to be -1

Answer 7

you'll get \[e^x (x-1)\]

Answer 8

mmhmm

Answer 9

substitute infinity?

Answer 10

-1

Answer 11

did you substitute to \(-\infty\) @.Sam. ?

Answer 12

you can actually evaluate some integrals at infinity. This one happens to be one.

when you sub x = - infinity into e^x(x-1) you get
e^(-infinity)(-infinity - 1)

this can be rewritten as (-infinity - 1)/[e^(infinity)]
the exponential function grows much faster than the linear function, so this will evaluate to 0. (its more of a limit calculation than anything, but too lazy to type that out)

Answer 13

@.Sam. is right. Just remember this:
| I --->Inverse trig
| L--->log function
| A--->algebraic function
| T----> Trig function
V E---> exponential functiom

ILATE -->Decreasing order of choice for u in u dv rule

Answer 14

i think logarithms should be used before inverse trigs according to this http://openstudy.com/study#/updates/4f9df983e4b000ae9ed2688c

but thanks all of you :D

Answer 15

Nope :) I am dead sure on this. . Wait . Let me tag @lgbasallote

Answer 16

Liate rule

A rule of thumb proposed by Herbert Kasube of Bradley University advises that whichever function comes first in the following list should be u:[1]
L: Logarithmic functions: ln x, logb x, etc.
I: Inverse trigonometric functions: arctan x, arcsec x, etc.
A: Algebraic functions: x2, 3x50, etc.
T: Trigonometric functions: sin x, tan x, etc.
E: Exponential functions: ex, 19x, etc.

Source: http://en.wikipedia.org/wiki/Integration_by_parts

Haha sorry :PP jkjk

Answer 17

@lgbasallote , why don't you take an example and check for yourself ? :)

Answer 18

take an example?

Answer 19

http://math.stackexchange.com/questions/10146/intuition-behind-the-ilate-rule

Answer 20

http://www.johndcook.com/blog/2008/02/28/what-to-make-u-in-integration-by-parts/

Answer 21

taking u as a inverse trig function over a logarithmic function would led to a nasty nasty derivative. They maybe few cases where the inverse trig function as your u may be better but for at least 90% of your problems you should take logs first.

Answer 22

@lgbasallote , There are two rules
1) LIATE rule
2) ILATE rule

Use you experience while doing integration. :)

Answer 23

@alexandercpark agrees with me :P and logarithms are ALMOST impossible to integrate haha

Answer 24

Let me search for an example. :D

Answer 25

i accept the challenge then >:))