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Mathematics 77 Online
OpenStudy (anonymous):

integrate 2e^(t-2)x

OpenStudy (amistre64):

you sure?

OpenStudy (anonymous):

yes

OpenStudy (amistre64):

whats the variable to integrate by? x or t?

OpenStudy (anonymous):

dx

OpenStudy (amistre64):

k.... the t-2 would act like a constant

OpenStudy (anonymous):

(2e^(t-e)x)(1/(t-2)?

OpenStudy (amistre64):

take the 2 to the outside since its a constant

OpenStudy (amistre64):

then multiply by (t-2)/(t-2) and take the bottom one out since its acting like a constant as well

OpenStudy (amistre64):

and we int((t-2) e^(t-2)x) which = e^(t-2)x bring over the constants to get: 2 e^(t-2)x --------- (t-2)

OpenStudy (amistre64):

... +c lol

OpenStudy (anonymous):

why are you multiplying top and bottom by t-2

OpenStudy (anonymous):

\[2(xe ^{t-2} - e ^{t-2})+c\]

OpenStudy (amistre64):

because I know how to int (t-2) e^(t-2)x; so I need to use a useful form of '1' to help me out..

OpenStudy (amistre64):

(t-2)/(t-2) = 1 so the value of the function stays the same; only thing that changes is the way it looks

OpenStudy (anonymous):

wait so that "x" was "dx"?

OpenStudy (anonymous):

how do you integrate this int (t-2) e^(t-2)x

OpenStudy (amistre64):

and the way it looks is important to me... becasue I can int (t-2) e^(t-2)x :) the rest is just constants that can be dragged outside right?

OpenStudy (anonymous):

integrating wrt x

OpenStudy (amistre64):

t-2 = say...u u e^ux ints up to e^ux

OpenStudy (anonymous):

oh you have to use u-sub for this problem?

OpenStudy (amistre64):

you can if it helps to see whats going on, but yeah....

OpenStudy (amistre64):

u sub is just a way to clean up the function to see it better; gets the distracting stuff out the way

OpenStudy (anonymous):

so putting it in that form is the easiest way to solve?

OpenStudy (amistre64):

integration is not an 'easy' thing. it is an art more than a science

OpenStudy (amistre64):

t-2 = u {S} 2 e^ux dx 2 {S} e^ux dx 2 {S} (u/u) e^ux dx 2/u {S} u e^ux dx (2/u) e^ux

OpenStudy (amistre64):

.... +C

OpenStudy (anonymous):

so you're integrating 2e^ux?

OpenStudy (amistre64):

yes, but recall that i defined u = t-2; and the t-2 is acting like a constant

OpenStudy (anonymous):

yeah. i think i need to play around with similar problems and practice

OpenStudy (anonymous):

thanks!

OpenStudy (amistre64):

yw :)

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