In certain species of flour beetles, the larvae cannibalize the unhatched eggs. In calculating the population cannibalism

Question:

In certain species of flour beetles, the larvae cannibalize the unhatched eggs. In calculating the population cannibalism rate per egg, researchers needed to evaluate the integral

where A is the length of the larval stage and c(x) is the cannibalism rate per egg per larva of age x. The minimum value of A for the flour beetle Tribolium castaneum is 17.6 days, which is the value we will use. The function c(x) starts at day 0 with a value of 0, increases linearly to the value 0.024 at day 12, and then stays constant. Find the values of the integral using
(a) Formulas from geometry;
(b) The Fundamental Theorem of Calculus.

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