(FTOC) Evaluate the integral:
(x-1)/x^(1/2) dx, [9,1]
Answer: -40/3
Me: 12

(x-1)/x^(1/2) dx = (1/2)x^(3/2) - (1/2)x^(1/2)

so: [(1/2)(9)^(3/2) - (1/2)(9)^(1/2)] - [(1/2)(1)^(3/2) - (1/2)(1)^(1/2)
= [(27/2)-(3/2)] - [0]
=12
I must be doing something wrong on doing the (1/2)x^(3/2) - (1/2)x^(1/2) but I can not figure it out.

Question

(FTOC) Evaluate the integral:
(x-1)/x^(1/2) dx, [9,1]
Answer: -40/3
Me: 12

(x-1)/x^(1/2) dx = (1/2)x^(3/2) - (1/2)x^(1/2)

so: [(1/2)(9)^(3/2) - (1/2)(9)^(1/2)] - [(1/2)(1)^(3/2) - (1/2)(1)^(1/2)
= [(27/2)-(3/2)] - [0]
=12
I must be doing something wrong on doing the (1/2)x^(3/2) - (1/2)x^(1/2) but I can not figure it out.

anonymous · Answer

$$\int\limits_{1}^{9} \frac{ x-1 }{\sqrt{x}  } dx$$

anonymous · Answer

Simplify it first:
              ( x - 1 )/ √x     =  x^½   -  x ^(-½)
    ∫ ( x½  -  x ^(-½) ) dx =   ⅔ x^3/2   - 2x^½      [ 1, 9 ]
=    ⅔ [ 9^(3/2)  - 1 ]   - 2 [ 3 - 1 ]
=     ⅔ [   27      - 1 ]   -  4
=              52/ 3          - 12/3            = 40/3