Evaluate the integral using the FTC I

**Lisa30907** · Jul 7th 2009, 04:49 AM

t-1/square root of t dt

the integral is from 1 to 27 or 27
1

**malaygoel** · Jul 7th 2009, 05:00 AM

Originally Posted by Lisa30907

t-1/square root of t dt

the integral is from 1 to 27 or 27
1

Is it
$\int_1^{27}\frac{t-1}{\sqrt t}dt$

or

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

And what is FTC?

**Lisa30907** · Jul 7th 2009, 05:10 AM

THE FIRST ONE

fundamental theorem of calculus

**skeeter** · Jul 7th 2009, 05:15 AM

Originally Posted by Lisa30907

THE FIRST ONE

fundamental theorem of calculus

$\frac{t-1}{\sqrt{t}} = \frac{t}{\sqrt{t}} - \frac{1}{\sqrt{t}} = t^{\frac{1}{2}} - t^{-\frac{1}{2}}<br />$

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

can you proceed from this point?

**malaygoel** · Jul 7th 2009, 05:19 AM

$\frac{t}{\sqrt t}=\sqrt t$

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

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

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

Can you do now???

**Lisa30907** · Jul 7th 2009, 05:29 AM

im working on it

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