Answer
14
Work Step by Step
Sketch:
Linear function: $f(x)=3x+4$, bounds: x=0 to x=2.
(see below)
We see a trapezoid,
with (vertical) bases 4 and 10,
and the height (from base to base) of 2.
$A=\displaystyle \frac{b_{1}+b_{2}}{2}h=(\frac{4+10}{2})\cdot 2=7\cdot 2=14$
$A=\displaystyle \int_{0}^{2}(3x+4)dx=14$
