1. ## Quick Intergration question

How would i complete the following question:

Find $\displaystyle \int_{-1}^{2}x+2f(x)dx if \int_{-1}^{2}f(x)dx=5$

P.S

2. Originally Posted by Paymemoney
How would i complete the following question:

Find $\displaystyle \int_{-1}^{2}x+2f(x)dx if \int_{-1}^{2}f(x)dx=5$

P.S
...from what I understand of the above integration, you could simply separate
$\displaystyle \int_{-1}^{2}x+2f(x)dx = \int_{-1}^{2}xdx+2\int_{-1}^{2}f(x)dx$

of which the later is given

3. $\displaystyle \int_{-1}^{2}x+2f(x)~dx$

with

$\displaystyle \int_{-1}^{2}f(x)~dx=5$

take $\displaystyle \int_{-1}^{2}x+2f(x)~dx$ apart into separate integrals

$\displaystyle \int_{-1}^{2}x+2f(x)~dx$

$\displaystyle \int_{-1}^{2}x~dx+ 2\int_{-1}^{2}f(x)~dx$

using

$\displaystyle \int_{-1}^{2}f(x)~dx=5$

gives

$\displaystyle \int_{-1}^{2}x~dx+ 2\times 5$

Can you finish it from here?

4. Originally Posted by sym0110
...from what I understand of the above integration, you could simply separate
$\displaystyle \int_{-1}^{2}x+2f(x)dx = \int_{-1}^{2}xdx+\int_{-1}^{2}f(x)dx$

of which the later is given
You mean
$\displaystyle \int_{-1}^{2}x+2f(x)dx = \int_{-1}^{2}xdx+2\int_{-1}^{2}f(x)dx$

5. why do you go 2 X 5??

6. Originally Posted by Paymemoney
why do you go 2 X 5??
The second term in the answer is
$\displaystyle 2\int_{-1}^2 f(x)dx$

and you said, in your first post, that
$\displaystyle \int_{-1}^2 f(x)dx= 5$!