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Chapter 4: Q. 3 (page 398)
Use a definite integral to express the function whose output
at any real number x is the signed area between the
graph of and the on .
The definite integral is
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If f is negative on [鈭�3, 2], is the definite integral positive or negative? What about the definite integral 鈭� ?
Explain why it would be difficult to write the sum in sigma notation.
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.
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.
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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