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  1. For each function listed, do the following. Plot each function to verify that it is non-negative over the interval in question. Determine the area under the curve using the int command. Choose one of the three rectangular approximations leftsum, rightsum or middlesum and determine the minimum number of subintervals required so that the approximation agrees with the integral to the fourth decimal place. Don't use the same rectangular approximation method for every part; please use each method at least once.
    1. tex2html_wrap_inline295 on the interval [0,5].
    2. tex2html_wrap_inline299 on the interval [-4,4].
    3. tex2html_wrap_inline303 on the interval [-1,1].

  2. Use the Maple int command to work the following problems. Explain your ``setup" for each problem.
    1. Find the average value of the function tex2html_wrap_inline307 on the interval [-5,-1].
    2. Find the area between tex2html_wrap_inline311 and tex2html_wrap_inline313 on the interval tex2html_wrap_inline315 .
    3. Find the general anti-derivative of


  3. Let tex2html_wrap_inline317

    1. Approximate I by tex2html_wrap_inline321 for n = 20, 60 and 100.
      Approximate I by tex2html_wrap_inline327 for n = 20, 60 and 100.
      Approximate I by tex2html_wrap_inline333 for n = 20, 60 and 100.
    2. Write a paragraph summarizing your experience in this problem. (Feel free to run additional lines of Maple if you need to.) What approximation method seems to be the most accurate? Include at least one more insight you have gained from this exercise.
  4. Use Maple to compute the following definite and indefinite integrals.
    1. tex2html_wrap_inline337
    2. tex2html_wrap_inline339
    3. tex2html_wrap_inline341 , where n is a positive constant.
    4. tex2html_wrap_inline345
    5. tex2html_wrap_inline347
    6. tex2html_wrap_inline349

Roxanne Tisch
Thu Mar 27 08:41:19 EST 1997