Answer
a) 0
b) -8
c) -12
d) 10
e) -2
f) 16
Work Step by Step
a) $\int^{2}_{2}g(x)dx=0$ (for zero width interval, integral=0)
b) $\int^{1}_{5}g(x)dx=-\int^{5}_{1}g(x)dx=-8$
c) $\int^{2}_{1}3f(x)dx=3\int^{2}_{1}f(x)dx $
$=3\times-4=-12$
d) $\int^{5}_{2}f(x)dx=\int^{5}_{1}f(x)dx-\int^{2}_{1}f(x)dx $
$=6-(-4)=10$
e) $\int^{5}_{1}[f(x)-g(x)]dx $
$=\int^{5}_{1}f(x)dx-\int^{5}_{1}g(x)dx=6-8=-2$
f) $\int^{5}_{1}[4f(x)-g(x)]dx $
$=4\int^{5}_{1}f(x)dx-\int^{5}_{1}g(x)dx $
$=4\times6-8=16$
