You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an alternative browser.
You should upgrade or use an alternative browser.
Evaluate the Definate Integral
- Thread starter KEYWEST17
- Start date
Sorry, that's incorrect.
Perhaps try it this way. Breaking it up into easier integrations.
\(\displaystyle \int_{1}^{7}\frac{8x^{2}+10}{\sqrt{x}}dx=8\int_{1}^{7}x^{\frac{3}{2}}dx+10\int_{1}^{7}x^{\frac{-1}{2}}dx\)
Another way would be to make the sub \(\displaystyle x=u^{2}, \;\ dx=2udu\)
This results in an easy integration. Don't forget to change the integration limits, though.
Perhaps try it this way. Breaking it up into easier integrations.
\(\displaystyle \int_{1}^{7}\frac{8x^{2}+10}{\sqrt{x}}dx=8\int_{1}^{7}x^{\frac{3}{2}}dx+10\int_{1}^{7}x^{\frac{-1}{2}}dx\)
Another way would be to make the sub \(\displaystyle x=u^{2}, \;\ dx=2udu\)
This results in an easy integration. Don't forget to change the integration limits, though.
\(\displaystyle \int_{1}^{7}\frac{8x^{2}+10}{\sqrt{x}}dx\)
Let \(\displaystyle x=u^{2}, \;\ dx=2udu\)
This changes the integration limits to \(\displaystyle 1 \;\ and \;\ \sqrt{7}\)
\(\displaystyle \int_{1}^{\sqrt{7}}\frac{8u^{4}+10}{u}\cdot 2udu\)
\(\displaystyle =\int_{1}^{\sqrt{7}}\left(4(4u^{4}+5)\right)du\)
\(\displaystyle =\left \frac{4u(4u^{4}+25)}{5}}\right|_{1}^{\sqrt{7}}=\frac{4(221\sqrt{7}-29)}{5}\approx 444.569\)
Let \(\displaystyle x=u^{2}, \;\ dx=2udu\)
This changes the integration limits to \(\displaystyle 1 \;\ and \;\ \sqrt{7}\)
\(\displaystyle \int_{1}^{\sqrt{7}}\frac{8u^{4}+10}{u}\cdot 2udu\)
\(\displaystyle =\int_{1}^{\sqrt{7}}\left(4(4u^{4}+5)\right)du\)
\(\displaystyle =\left \frac{4u(4u^{4}+25)}{5}}\right|_{1}^{\sqrt{7}}=\frac{4(221\sqrt{7}-29)}{5}\approx 444.569\)
D
Deleted member 4993
Guest
or the otherway:
\(\displaystyle \int_{1}^{7}\frac{8x^{2}+10}{\sqrt{x}}dx=8\int_{1}^{7}x^{\frac{3}{2}}dx+10\int_{1}^{7}x^{\frac{-1}{2}}dx \ = \ 8*\frac{2}{5} \left [x^{\frac{5}{2}}\right ] \right|_1^7 \ + 10*2\left [x^{\frac{1}{2}}\right ] \right|_1^7 \ = \ \frac{16}{5}*[49\sqrt{7} -1] \ + \ 20*[\sqrt{7}-1]\)
and simplify......
\(\displaystyle \int_{1}^{7}\frac{8x^{2}+10}{\sqrt{x}}dx=8\int_{1}^{7}x^{\frac{3}{2}}dx+10\int_{1}^{7}x^{\frac{-1}{2}}dx \ = \ 8*\frac{2}{5} \left [x^{\frac{5}{2}}\right ] \right|_1^7 \ + 10*2\left [x^{\frac{1}{2}}\right ] \right|_1^7 \ = \ \frac{16}{5}*[49\sqrt{7} -1] \ + \ 20*[\sqrt{7}-1]\)
and simplify......
Subhotosh Khan & lookagain edit said:or the otherway:
\(\displaystyle \int_{1}^{7}\frac{8x^{2} + 10}{\sqrt{x}}dx\)
\(\displaystyle =8\int_{1}^{7}x^{\frac{3}{2}}dx + 10\int_{1}^{7}x^{\frac{-1}{2}}dx \ =\)
\(\displaystyle \ 8*\frac{2}{5} \left [x^{\frac{5}{2}}\right ] \right|_1^7 \ + 10*2\left [x^{\frac{1}{2}}\right ] \right|_1^7 \ =\)
\(\displaystyle \ \frac{16}{5}*[49\sqrt{7} -1] \ + \ 20*[\sqrt{7} -1]\)
and simplify......
The last few characters of your line did not get shown because of the margin
cutting it off, so I sent it down away from the right margin so it can be seen.