Review Sheet –Math 202-Test 3
Review Sheet –Math 202-Test 3
Chapter 14
1. Be able to reverse the differentiation process and find anti-derivatives and indefinite integrals through rules
summarized on page 625 and 638. Recognize that indefinite integrals involve the inclusion of a constant.
• Be able to reverse a differentiation that involved the chain rule through use of substitution.
• Be able to use algebraic techniques to rewrite functions in a form more easily integrated. Such techniques include:
o Multiplication of factors;
o Moving a constant into or out of an integral;
o Breaking a rational expression of the form [pic] into separate fractions of the form [pic] or divide a polynomial denominator into the numerator and integrate the quotient and remainder (stated as a fraction).
o Use of the exponential relationship a = eln a.
2. Be able to find a specific anti-derivative when given a general anti-derivative and information that leads to
identification of the constant.
3. Be able to work with summation techniques and formulas presented in Section 1.5.
4. Be able to approximate the area trapped by a curve, the x axis and a vertical line by dividing the region into n rectangles, all with consistent width and height dependent on the function. Then add the areas of the rectangles as
[pic] to approximate the given area.
5. Be able to find a definite integral by taking the limit of the summation of the area of rectangular pieces as the number
of pieces approaches infinity, that is [pic] . (Note: as the number of pieces approaches infinity, the width of each
piece approaches zero.)
6. Understand and be able to work with the Fundamental Theorem of Integral Calculus stated on page 653 which
states [pic] where f(x) is continuous on [a, b] and F(x) is any anti-derivative of f(x).
• Be able to work with properties of definite integrals stated on pages 654 and 655.
• Recognize that the definite integral of f(x) over [a, b] represents the area trapped by the curve, the x axis and vertical lines x = a and x = b as long as f(x) is positive in the interval. Be able to find such an area.
o If f(x) is negative over a portion or over all of an interval, absolute value must be applied to the negative portion.
7. Be able to find the area trapped between two curves over a given interval.
8. Be able to work with practical applications of the above concepts.
9. Be able to find Consumers Surplus and/or Producers Surplus in a given situation.
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