t-1/square root of t dt the integral is from 1 to 27 or 27 1
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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?
THE FIRST ONE fundamental theorem of calculus
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?
$\displaystyle \frac{t}{\sqrt t}=\sqrt t$ 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???
im working on it
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