Question

http://tutorial.math.lamar.edu/classes/calcII/IntegrationByParts_files/eq0020M.gif
I wanna know how this has done
Thanks

Answer 1

no actually it ha to integration by parts

Answer 2

Integration by parts! :)
Let f=x and g'=e^(6x)
=>
f'=1 g=e^(6x)/6

Answer 3

\[\int\limits_{}^{}fg' dx=fg-\int\limits_{}^{}f'gdx\]

Answer 4

plug it in! :)

Answer 5

i got the answer but I don't know how it has done

Answer 6

I don't know how to do the last part of this problem

Answer 7

\[x \cdot \frac{e^{6x}}{6}-\int\limits_{}^{}1 \cdot \frac{e^{6x}}{6} dx\]
so do you understand this part?

Answer 8

all i did was plug in

Answer 9

yeah i did but i don't know how they got 11 and 7

Answer 10

\[\frac{xe^{6x}}{6}-\frac{1}{6}\int\limits_{}^{}e^{6x} dx=\frac{xe^{6x}}{6}-\frac{1}{6} \cdot \frac{1}{6} e^{6x}+C\]

Answer 11

so you are actually find with the integrating then
you are having trouble plugin and the limits and simplifying?

Answer 12

fine not find

Answer 13

i got same your answer but I have different answer in this site

Answer 14

\[\int\limits_{-1}^{2}xe^{6x} dx=[\frac{xe^{6x}}{6}-\frac{1}{36}e^{6x}]_{-1}^{2}\]

Answer 15

\[=[\frac{2e^{6(2)}}{6}-\frac{e^{6(2)}}{36}]-[\frac{-1e^{6(-1)}}{6}-\frac{e^{6(-1)}}{36}]\]

Answer 16

\[=\frac{1e^{12}}{3}-\frac{e^{12}}{36}+\frac{e^{-6}}{6}+\frac{e^{-6}}{36}\]

Answer 17

\[=\frac{12-1}{36}e^{12}+\frac{6+36}{36}e^{-6} \]
\[=\frac{11}{36}e^{12}+\frac{42}{36}e^{-6}=\frac{11}{36}e^{12}+\frac{7}{6}e^{-6}\]

Answer 18

Thank you very much Myininaya
Can you see the answer ?

Answer 19

oh i see where i made a mistake

Answer 20

do you see my mistake?

Answer 21

so we have this
\[=[\frac{2e^{6(2)}}{6}-\frac{e^{6(2)}}{36}]-[\frac{-1e^{6(-1)}}{6}-\frac{e^{6(-1)}}{36}] \]

Answer 22

\[=\frac{12-1}{36}e^{12}-\frac{-6-1}{36}e^{-6}\]

Answer 23

there we go

Answer 24

lol i wrote 1/36 as 36/36 above thats why it came out wrong the first try

Answer 25

yeah that make sense but how did you get 12

Answer 26

common denomaintor?

Answer 27

\[\frac{2}{6} \cdot \frac{6}{6}=\frac{12}{36}\]

Answer 28

yeah that make sense to me
You help me a lot
I really thank you so much that was very helpful to me

Answer 29

np