Calculator Assignments due in recitation
Make sketches of the calculator screen and hand those in when
called for. Be sure to indicate the axis scales on any sketch.

1.)  Graph the function f(x) = sin((x^2)/2) in the viewing rectangle [0,1] by
[0, 0.5] and let I denote the integral from 0 to 1 of f(x).
Consider the following types of approximate integration:
Left End Point(n) = LEP(n) using n-subintervals
  (if n = 2 the you would use the rule twice from 0 to 0.5 and then from
  0.5 to 1 and add the results.)
Right End Point(n) = REP(n)
Midpoint(n) = M(n)
Trapezoidal(n) = T(n)
a.)  Use the graph to decide whether L(2), R(2), M(2) and T(2) are
overestimates or underestimates for I.
b.)  Do the same thing for L(n), R(n), M(n) and T(n) for any value of n
c.)  For the case n=5 try to estimate which method give the best result.


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2.)  Evaluate | ln(x^2 + 2*x + 2) dx and graph both the integrand and the
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indefinite integral (in the case C=0) to check that you answer for the
integral is reasonable.  Hand in the graphs.


3.)  Graph the function f(x) = (cos(x))^2*(sin(x))^3 in the range from 0 to
2*Pi.  Use your graph to guess the value of the integral of f(x) over that
region.  Next evaluate the integral and confirm your guess in the first
part of this problem.