# Evaluate the integral using the FTC I

• Jul 7th 2009, 04:49 AM
Lisa30907
Evaluate the integral using the FTC I
t-1/square root of t dt

the integral is from 1 to 27 or 27
1
• Jul 7th 2009, 05:00 AM
malaygoel
Quote:

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?
• Jul 7th 2009, 05:10 AM
Lisa30907
THE FIRST ONE

fundamental theorem of calculus
• Jul 7th 2009, 05:15 AM
skeeter
Quote:

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?
• Jul 7th 2009, 05:19 AM
malaygoel
$\displaystyle \frac{t}{\sqrt t}=\sqrt t$

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???
• Jul 7th 2009, 05:29 AM
Lisa30907
im working on it