Answer
$\dfrac{40}{3}$
Work Step by Step
We are given that $I=\int_0^{4} |-3x+4| \ dx$
In order to solve the above integral, we will use the following formula such as:
$\int |ax+b| \ dx=\dfrac{1}{2a}(ax+b)|ax+b|+C$
Now, we have $I=[\dfrac{1}{(2)(-3)} (-3x+4)|-3x+4|]_0^4 $
or, $=-\dfrac{1}{6}[(-3x+4)|-3x+4|]_0^4 $
or, $=-\dfrac{1}{6}[(-3(4)+4)|-3(4)+4|]-\dfrac{1}{6}[(-3(4)+4)|-3(4)+4|]$
or, $=-\dfrac{1}{6}(-64-16)$
or, $=\dfrac{40}{3}$
