Question on integration of exponentials (1 Viewer)

[karnage]

Just a small question im stuck on (last question for HW then im done! )

a) Differentiate xe^x

Pretty sure i got this part covered.
d/dx = xe^x + e^x
= e^x (x + 1)

b) Hence find ∫ 2 to 0 xe^x dx

Not sure on this part as i keep on getting the wrong answer (i assumed hence was the key word that part a had something to do with this part). If you maths guru's could please enlighten me on what to do as i am not the best at mathematics. Much appreciated :uhhuh:

 

[pLuvia]

Haven't answered maths questions in ages

Since this is 2 unit, just part a) to do part b)

d/dx(xe^x)=xe^x+e^x
xe^x=d/dx(xe^x)-e^x
int. {0 to 2}xe^xdx=[xe^x]{0 to 2}-int. {0 to 2}e^xdx

Then you just go from there

 

[Mark576]

d/dx (xe^x) = xe^x + e^x
∫(xe^x + e^x) dx = ∫(xe^x) dx + ∫e^x dx
=> xe^x = ∫xe^x dx + e^x
=> ∫xe^x dx = [xe^x - e^x]

Remembering this is all considered with the upper and lower bounds omitted for simplification.

Finally just evaluate the expression [xe^x - e^x] from x = 2 to x = 0

EDIT: Damn, not fast enough

 

[karnage]

Thanks alot for the quick reply.

Just the remaining working out for the sake of it.
int.{0 to 2} xe^x - e^x dx
= [ xe^x - e^x ] {0 to 2}
= ( 2e^2 - e^2 ) - ( 0 - 1)
= e^2 + 1

Hope that looks right, because its the right answer

On a side note, how did you do the superscript for the x.

Hmmm brains. Where can i get one of those?

 

[pLuvia]

It's just the codes

[sup ] TEXT [/sup ] without the spaces