Quick Intergration question

**Paymemoney** · December 31st 2009, 02:09 PM

How would i complete the following question:

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

P.S

**sym0110** · December 31st 2009, 02:15 PM

Originally Posted by Paymemoney

How would i complete the following question:

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

P.S

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

of which the later is given

**pickslides** · December 31st 2009, 02:17 PM

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

with

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

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

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

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

using

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

gives

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

Can you finish it from here?

**pickslides** · December 31st 2009, 02:20 PM

Originally Posted by sym0110

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

of which the later is given

You mean
$\int_{-1}^{2}x+2f(x)dx = \int_{-1}^{2}xdx+2\int_{-1}^{2}f(x)dx$

**Paymemoney** · December 31st 2009, 03:16 PM

why do you go 2 X 5??

**HallsofIvy** · January 1st 2010, 05:22 AM

Originally Posted by Paymemoney

why do you go 2 X 5??

The second term in the answer is
$2\int_{-1}^2 f(x)dx$

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

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