The boxes can weight at most 5 grams less than the desired amount, so they can't be lighter than
grams
Similary, they can't weight more than 5 grams more than the desired amount, so they can't be heavier than
grams
So, the acceptable range is between 208 and 218.
Find where the curve intersects the <em>x</em>-axis; this happens when <em>y</em> = 0:
<em>y</em> = <em>t</em> - <em>t</em> ² = 0 → <em>t</em> (1 - <em>t</em> ) = 0 → <em>t</em> = 0, <em>t</em> = 1
Then the area of the bounded region is
(you can compute the integral by parts)
