Answer
a. $8$
b. $-12$
c. $-4$
d. $30$
Work Step by Step
a.
$\displaystyle \int_{2}^{6}[f(x)+g(x)]dx$ = (...Th. 4.7.2 )
$=\displaystyle \int_{2}^{6}f(x)dx+\int_{2}^{6}g(x)dx=10+(-2)=8$
b.
$\displaystyle \int_{2}^{6}[g(x)-f(x)]dx$ = (... Th. 4.7.2)
$=\displaystyle \int_{2}^{6}g(x)dx-\int_{2}^{6}f(x)dx=-2-10=-12$
c.
$\displaystyle \int_{2}^{6}2g(x)dx$= (... Th. 4.7.1)
$=2\displaystyle \int_{2}^{6}g(x)dx=2(-2)=-4$
d.
$\displaystyle \int_{2}^{6}3f(x)dx$= (... Th. 4.7.1)
$=3\displaystyle \int_{2}^{6}f(x)dx=3(10) =30$
