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
$\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?