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Chapter 4: Q. 11 (page 362)
Write out all the integration formulas and rules that we know at this point.
The formulas are:
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Prove part (b) of theorem 4.4 in the case when n is even: if n is a positive even integer, then
Use integration formulas to solve each integral in Exercises 21鈥�62. You may have to use algebra, educated guess- and- check, and/or recognize an integrand as the result of a product, quotient, or chain rule calculation. Check each of your answers by differentiating. (Hint for Exercise 54: ).
Calculate the exact value of each definite integral in Exercises 47鈥�52 by using properties of definite integrals and the formulas in Theorem 4.13.
Show by exhibiting a counterexample that, in general, . In other words, find two functions f and g so that the integral of their product is not equal to the product of their integrals.
Shade in the regions between the two functions shown here on the intervals (a) [鈭�2, 3]; (b) [鈭�1, 2]; and (c) [1, 3]. Which of these regions has the largest area? The smallest?
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