1. ## Another Integral Question

$
\int \frac{{{2x}^2+2}}{x^2}dx
$

There's an upper limit of 4 and lower limit of 1.

2. Originally Posted by Lolcats
$
\int \frac{{{2x}^2+2}}{x^2}dx
$

There's an upper limit of 4 and lower limit of 1.

Note that $\frac{2x^2+2}{x^2}=2+2x^{-2}$

So, can you find $\int_1^4(2+2x^{-2})dx$ ?

3. Originally Posted by Lolcats
$
\int \frac{{{2x}^2+2}}{x^2}
$

There's an upper limit of 4 and lower limit of 1.
Hello .
$\frac{{{2x}^2+2}}{x^2}=\frac{2x^2}{x^2}+\frac{2}{x ^2}$
$=2+2x^{-2}$
Now,
$\int_{1}^{4} \frac{{{2x}^2+2}}{x^2} dx$
$=2\int_{1}^{4}dx+2\int_{1}^{4}x^{-2}dx$.

Can you complete it ?

4. Jeez these are easy problems I'm screwing up. Thanks !

5. Sorry to be a bother, the answer should be 4 shouldn't it?

6. Originally Posted by Lolcats
Sorry to be a bother, the answer should be 4 shouldn't it?
No.
See this:
integrate [ 2 + 2 x^(-2) ] from x=1 to x=4 - Wolfram|Alpha

7. Originally Posted by Lolcats
Sorry to be a bother, the answer should be 4 shouldn't it?
no

$15/2$

8. K well i'd integrate and get 2x-(2/x), then insert the upper limit so:
2(4) + 2/4 = 4 then minus that from 2(1) + 2/1 = 0

Sorry i'm replying slow I have a seperated shoulder atm and can only type with 1 hand.

9. Originally Posted by Lolcats
K well i'd integrate and get 2x-(2/x), then insert the upper limit so:
2(4) + 2/4 = 4 then minus that from 2(1) + 2/1 = 0

Sorry i'm replying slow I have a seperated shoulder atm and can only type with 1 hand.

See the red.

10. Wops.. thats embarrasing. Thanks again.