Calculus question

Question

A graph of ff is shown above. Estimate the following integral.

∫18

1f(x)dx

Answer 1

Basically, you need to measure area under the curve, starting from x=0 to x=18. The width and height of each rectangle in the grid seems to be one unit. First count the number of rectangles that are completely under the curve, and add to that estimated total area for those rectangles that are sliced by the curve.

Answer 2

Hi Mani P.,

You could do this the long and painful way (toting up squares) or the short and elegant way (examining the function shape, guessing the function, checking that the f(5) is = f(20)/2 (which it is, within visual interpolation), thus confirming that f(x) = k*x^0.5, (or, kx=y^2, a parabola opening to the right, rather than upwards!), estimating your best value for k, and just integrating). Which would you prefer? Long and painful or short and elegant?

P.S. Looking to classify your problems in the form of things you already know is generally a winning technique!

-- Cheers, --Mr. d.