# Thread: Evaluate the integral using the FTC I

1. ## Evaluate the integral using the FTC I

t-1/square root of t dt

the integral is from 1 to 27 or 27
1

2. Originally Posted by Lisa30907
t-1/square root of t dt

the integral is from 1 to 27 or 27
1
Is it
$\displaystyle \int_1^{27}\frac{t-1}{\sqrt t}dt$

or

$\displaystyle \int_1^{27}t-\frac{1}{\sqrt t}dt$??

And what is FTC?

3. THE FIRST ONE

fundamental theorem of calculus

4. Originally Posted by Lisa30907
THE FIRST ONE

fundamental theorem of calculus
$\displaystyle \frac{t-1}{\sqrt{t}} = \frac{t}{\sqrt{t}} - \frac{1}{\sqrt{t}} = t^{\frac{1}{2}} - t^{-\frac{1}{2}}$

$\displaystyle \int_1^{27} t^{\frac{1}{2}} - t^{-\frac{1}{2}} \, dt$

can you proceed from this point?

5. $\displaystyle \frac{t}{\sqrt t}=\sqrt t$

and its anti-derivative is $\displaystyle \frac{2}{3}t^{\frac{3}{2}}$

$\displaystyle \frac{1}{\sqrt t}=t^{\frac{-1}{2}}$

and its anti-derivative is $\displaystyle 2t^{\frac{1}{2}}$

Can you do now???

6. im working on it