I'm stuck on this problem, involving Definite Integrals and the Fundamental Theorem of Calculus. The problem:

"Evaluate: (integral)[(x-1)/(sqrt.x)]dx, from 1 to 9."

Any and all help is greatly appreciated!

Question

I'm stuck on this problem, involving Definite Integrals and the Fundamental Theorem of Calculus. The problem:

"Evaluate: (integral)[(x-1)/(sqrt.x)]dx, from 1 to 9."

Any and all help is greatly appreciated!

amonoconnor · Answer

Basically, I don't know how to find F(x) from f(x)... I'm not sure how to take the anti-derivative, so I can plug in the limits, and solve, etc.

anonymous · Answer

divide each term by $\sqrt{x}$ then use the power rule backwards as before

amonoconnor · Answer

$$f(x) = x^{1/2} - x^{-1/2}  ??$$

amonoconnor · Answer

$$F(x) = \frac{2}{3}x^{3/2} - 2x^{1/2}$$  ??

anonymous · Answer

looks reasonable

anonymous · Answer

in fact it looks right too

anonymous · Answer

why the question marks?  exponents are your friends here

amonoconnor · Answer

True... I do love the power rule when numbers are pretty like this, I'm just tired, and was unsure of my answer lols.

triciaal · Answer

got the same result

amonoconnor · Answer

Thank you very much!

anonymous · Answer

yw

amonoconnor · Answer

40/3. BOOM! Thanks again guys:)