Let's say the numbers are "a" and "b"
thus
set the derivative to 0, and check the critical points, there's only one anyway
and do a first-derivative test, to see if it's a maximum
a) The first integral corresponds to the area under y = f(x) on the interval [0, 3], which is a right triangle with base 3 and height 5, hence the integral is
b) The integral is zero since the areas under the curve over [3, 4] and [4, 5] are equal but opposite in sign. In other words, on the interval [3, 5], f(x) is symmetric and odd about x = 4, so
c) The integral over [5, 9] is the negative of the area of a rectangle with length 9 - 5 = 4 and height 5, so
Then by linearity, we have
Measure of x is 74 degrees
258 cubic inches
Since the boxes are kind of on their own—>
First box: 7*2*12 = 168
Second box: 5*2*9=90
168+90 = 258
