Integration by Parts: Solving the Integral of Sqrt(x) * ln(x) with Limits 1 to 5

[intelli]

Homework Statement

integral limit 1 to 5

integral of sqrt x * lnx dx

a = 1
b= 5

Homework Equations

The Attempt at a Solution

2
x (-1 + 2 Log[x])
------------------
8

11.99604193 but its not right

 

[rock.freak667]

Not sure how you reached that answer but did you use

u=lnx and dv=x^1/2 dx ?

 

[intelli]

Not sure how you reached that answer but did you use

u=lnx and dv=x^1/2 dx ?

so is this right

du = 1/x dx

v = 3/2x^3/2

and plug into the parts formula?

 

[rock.freak667]

so is this right

du = 1/x dx

v = 3/2x^3/2

and plug into the parts formula?

v=2/3 x^3/2

check that back.

then yes put that into the formula.

 

[intelli]

v=2/3 x^3/2

check that back.

then yes put that into the formula.

yes so i get this is this right after integrating

2/3 x^3/2 ln x (between limits 1 to 5 ) - 4/9 x^3/2 (between limits 1 to 5) and

i get 9.602

 

[chriscolose]

yes so i get this is this right after integrating

2/3 x^3/2 ln x (between limits 1 to 5 ) - 4/9 x^3/2 (between limits 1 to 5) and

i get 9.602

Your calculus looks correct, but somehow you're not coming up with the right number. Re-check your computations and you should get approximately 7.47.