Math: Integral Help

[CaptainKahuna]

I need the integral from -1 to 4 of the following

Xdx / Sqrt(5+x)

Any help? I can't figure out how to do it. I need to know method as well as numerical answer. Actually, I can do the numerical answer on my own, but I need method. Thanks all!

 

[esun]

I don't remember a method to do that integral, but I just opened up an integral table and found a definition for the integral of:

(u du) / sqrt(a + bu) = [2 / (3b^2)](bu - 2a) * sqrt(a + bu) + C

You can use that.

EDIT:

You can use u-sub, but it's very tricky to get it off the top of your head (I used Maple's IntTutor). If you set

u = sqrt(5 + x)

Then the integral equals

(-10 + 2u^2)du

Which should be quite easy to solve. How to know to rearrange it like that is something I do not know.

 

[minendo]

The answer is always 4.

 

[CaptainKahuna]

Originally posted by: esun
I don't remember a method to do that integral, but I just opened up an integral table and found a definition for the integral of:

(u du) / sqrt(a + bu) = [2 / (3b^2)](bu - 2a) * sqrt(a + bu) + C

You can use that.

Thats a start, thanks.

I've tried U-Sub and COV, but I still cant get it. Anyone else with a method?

 

[Peetoeng]

It's been years since I do integration .

Using u-substitution:

Let's pick
u = 5 + x (eq. 1)

then
x = u - 5
du = dx


I = int( x dx / sqrt(5 + x) ) = int( (u-5)du / sqrt(u) )

Expand the integral
Res = int( u du / sqrt(u) ) + int( -5 du / sqrt(u) )
Res = int( u^0.5 du) - 5 int( u^-0.5 du)
which are easy to integrate.

Put the limits of intergration in terms of u,
x = -1 ---> u = see eq 1.
x = 4 ---> u = see eq. 1