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Up: The Definite Integral -
- For each of the following functions and intervals determine the
area under the curve with the int command. Also, choose one
of the three rectangular approximations leftsum,
middlesum or rightsum and determine the minimum
number of subintervals required so that your rectangular approximation
agrees with the integral to four decimal places. Don't use the same
rectangular approximation method for every part; please use each
method at least once. Also, plot each function to verify that it is
non-negative over the interval in question.
- Consider the function f(x) = -2x+8 on the interval [0,4]. Verify
that the middlesum command gives the exact value for the area
independently of the number of subintervals you specify. Can you
explain this? Hint - look at the graph produced by the
William W. Farr