`int_1^9((x - 1)/sqrt(x))dx` Evaluate the integral.

Expert Answers
Borys Shumyatskiy eNotes educator| Certified Educator

Hello!

Find the indefinite integral first:

`int((x-1)/sqrt(x))dx=int(x^(1/2)-x^(-1/2))dx=(2/3)*x^(3/2)-2*x^(1/2)+C.`

So the definite integral is equal to

`((2/3)*x^(3/2)-2*x^(1/2))|_(x=1)^(x=9)=((2/3)*27-6)-((2/3)-2)=12-2/3+2=13 and 1/3 approx 13.33.`