The graph of a piecewise linear function \(f(x)\) is above. Evaluate \(\displaystyle \int\limits_3^8 f'(x)   dx \)

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Though it may be tempting to take the area under the curve, it would not lead to our answer. We need to integrate \(f'(x)\) and use the graph to obtain our needed values.

$$ \int \limits_3^8 f'(x)   dx = f(x)\Big]_3^8 $$ $$ =f(8)-f(3) $$ $$ = 0 - 2 $$ $$ = \boxed{-2} $$