What are the degrees a trapezoid has?
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Hope you are able to understand the solution. :-D
Since the length is 10 in. You must multiply it by 
and then multiply by 
. The reason for this is because if you divide ten by 5 it will be 2, then if you divide 2 by 2 it will be 1.
The maxima of f(x) occur at its critical points, where f '(x) is zero or undefined. We're given f '(x) is continuous, so we only care about the first case. Looking at the plot, we see that f '(x) = 0 when x = -4, x = 0, and x = 5.
Notice that f '(x) ≥ 0 for all x in the interval [0, 5]. This means f(x) is strictly increasing, and so the absolute maximum of f(x) over [0, 5] occurs at x = 5.
By the fundamental theorem of calculus,
The definite integral corresponds to the area of a trapezoid with height 2 and "bases" of length 5 and 2, so