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You are suppose to make a pin that is 6 cm long. Unfortunately, the machine will produce pins that 6 + y cm long. where 0 <= y <= 2, and the function f(y) = K(y + y^2).

if the pin is more then 7 cm long, then it is unusable. Find the proportion that is produced that will be unusable.

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ok, so if y = 0, or y = 1, then it is fine, and if y = 2, then it is unusable.

so can I just integrate from 0 to 1 of f(y), and then subtract from 1, to get the answer?

the book says the answer is 23/28....but I dont know how it got that.