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Chapter 4: Q. 7 (page 351)
If f(x) is defined at x = a, then . Explain why this makes sense in terms of area.
m
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Show that is an antiderivative of .
If and ,then find the values of each definite integral in Exercises . If there is not enough information, explain why.
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Suppose on [1, 3] and on (鈭掆垶, 1] and [3,鈭�). Write the area of the region between the graphs of f and g on [鈭�2, 5] in terms of definite integrals without using absolute values .
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: ).
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Prove that in three different ways:
(a) algebraically, by calculating a limit of Riemann sums;
(b) geometrically, by recognizing the region in question as a trapezoid and calculating its area;
(c) with formulas, by using properties and formulas of definite integrals.
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