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evaluate integral 4 on top integal sign 0 at bottom e^3xdxI am also having trouble...

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jjmgingrich | Student, Undergraduate | Salutatorian

Posted July 20, 2012 at 4:23 AM via web

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evaluate integral 4 on top integal sign 0 at bottom e^3xdx

I am also having trouble inputing this into my TI-83 to solve any suggestions??

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted July 20, 2012 at 4:43 AM (Answer #1)

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Evaluate `int_0^4e^(3x)dx` :

Note that `inte^udu=e^u+C`

Let `u=3x,du=3` . When `x=0,u=0;x=4,u=12`

To make the integrand look like `e^(3x)3dx` we can mulitply by 3 and `1/3` to get:

`int_0^4e^(3x)(1/3)3xdx` or `1/3int_0^4e^(3x)3dx` .

Substituting for u, and changing the limits of integration we get:

`1/3int_0^12 e^udu=1/3[e^u|_0^12]=1/3[e^12-e^0]`

`~~1/3[162754.7914-1]~~54251.26`

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`int_0^4e^(3x)dx~~54251.26`

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** In the graphing calculator graph the function `y=e^((3x))` (Note the use of parantheses). Then hit 2nd trace;7;0;4 to see the area and the result. Use the `e^x` key instead of the `e` key.

If the function will not graph make sure your Stat Plots are off (Go into stat plot anfd hit 4 for plots off -- or in the y= screen you can arrow up to the highlighted plots and hit enter to turn them off.

Make sure your window includes the x values from 0 to 4 (at least)

Those are the most common errors I can think of.

 

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