I need to find the definite integral between 4 and 9 where the function is [1+sqrt(x)]/sqrt(x) dx Without using integration by parts. I got 35*1/3 but I'm sure the way I did this was wrong.
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You don't need parts or any other techniques, just plain ol' strightforward integration. $\displaystyle \frac{1+\sqrt{x}}{\sqrt{x}}=x^{\frac{-1}{2}}+1$ $\displaystyle \int_{4}^{9}\left[x^{\frac{-1}{2}}+1\right]dx=7$
Originally Posted by SportfreundeKeaneKent I need to find the definite integral between 4 and 9 where the function is [1+sqrt(x)]/sqrt(x) dx Without using integration by parts. I got 35*1/3 but I'm sure the way I did this was wrong. Or if you meant something like $\displaystyle \int_a^{b}\frac{(1+\sqrt{x})^n}{\sqrt{x}}dx=2\int_ a^b\frac{(1+\sqrt{x})^n}{2\sqrt{x}}dx=\frac{2(1+\s qrt{x})^{n+1}}{n+1}\bigg|_{a}^b$
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