Chapter 4: Q. 21 (page 325)
Write each of the sums in Exercises 21–28 in sigma notation. Identify in each problem.
The sigma notation is
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Use integration formulas to solve each integral in Exercises 21–62. 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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For each function f and interval [a, b] in Exercises 27–33, use the given approximation method to approximate the signed area between the graph of f and the x-axis on [a, b]. Determine whether each of your approximations is likely to be an over-approximation or an under-approximation of the actual area.
, n = 3 with
a) Trapezoid sim b) Upper sum
Shade in the regions between the two functions shown here on the intervals (a) [−2, 3]; (b) [−1, 2]; and (c) [1, 3]. Which of these regions has the largest area? The smallest?
Use the Fundamental Theorem of Calculus to find the exact values of the given definite integrals. Use a graph to check your answer.
Determine which of the limit of sums in Exercises 47–52 are infinite and which are finite. For each limit of sums that is finite, compute its value
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