Chapter 4: Q. 47 (page 353)
Calculate the exact value of each definite integral in Exercises 47–52 by using properties of definite integrals and the formulas in Theorem 4.13.
Short Answer
The exact value of definite integral is.
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Chapter 4: Q. 47 (page 353)
Calculate the exact value of each definite integral in Exercises 47–52 by using properties of definite integrals and the formulas in Theorem 4.13.
The exact value of definite integral is.
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Write each expression in Exercises 41–43 in one sigma notation (with some extra terms added to or subtracted from the sum, as necessary).
Compare the definitions of the definite and indefinite integrals. List at least three things that are different about these mathematical objects.
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.
left sum with
a) n = 3 b) n = 6
Use the Fundamental Theorem of Calculus to find the exact values of the given definite integrals. Use a graph to check your answer.
Prove Theorem 4.13(c): For any real numbers a and b, Use the proof of Theorem 4.13(a) as a guide.
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