integration

[rae27]

I'm having trouble with the integral sqrt [1+(e^x+xe^x)^2] from 1to 3. I've tired substitution and by parts, I'm not getting anywhere. Please help.

Thanks

 

[galactus]

$\displaystyle \int_{1}^{3}\sqrt{1+(e^{x}+xe^{x})^{2}}dx$

This one is not doable by elementray methods. I couldn't even get Maple to give me an indefinite form. I would suggest some sort of numerical method such as Simpson's Rule, Trapezoid Rule, etc.

 

[Deleted member 4993]

I'm having trouble with the integral sqrt [1+(e^x+xe^x)^2] from 1to 3. I've tired substitution and by parts, I'm not getting anywhere. Please help.

Thanks

Are you trying to find "length of the curve" y = x*e^x?

In case you are, the length from x=1 to x=3 is 57.6

 

[BigGlenntheHeavy]

Thanks galactus and Subhotosh Khan, as he is trying to find the arc length of x*e^x, and most of these arc length integrals can't be solved by elementary methods. Thanks again.

$\displaystyle f(x) \ = \ \int_{1}^{3}[1+(e^{x}+xe^{x})^{2}]^{1/2}dx \ = \ 57.5994781453$

Thank you trusty TI-89, as you saved me the drudgery of doing numerical integration.

 

[galactus]

Here is an approximation using the midpoint rule with 20 partitions. Like Glenn, I sure don't want to do it by hand.

This integral represents the arc length of $\displaystyle xe^{x}$ from 1 to 3.

Do not get it confused with the actual graph of $\displaystyle xe^{x}$

 

[BigGlenntheHeavy]

Here is one from Maple 8.


[attachment=1:mdaqqasu]xyz.jpg[/attachment:mdaqqasu]

Ok, I got it to animate on a gif. file.

[attachment=0:mdaqqasu]abc.gif[/attachment:mdaqqasu]