Problem Three:

In this problem, we are asked to find the area of a right triangle with an acute angle at the origin, an acute angle at the point, "fifty…twenty-five," and a right angle on the x-axis. The area is one half of the product base-times-height. You may work this number out for yourselves.
Using the integral calculus, we are asked to find the area between the x-axis and the line from the origin to the point, "fifty…twenty-five." The equation of this line is, "y equals fifty-over-twenty-five x," which simplifies to, "y equals one-half x." The corresponding integral is, "The integral from x-equals-zero to x-equals-fifty of one-half-x-dee-x." The value of this integral, using feet for our unit of measure, is six-hundred-and-twenty-five square feet.