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Chapter 4: Q. 16 (page 403)
Fill in the blanks to complete each sum formula:
The complete sum formula is
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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.
Without using absolute values, how many definite integrals would we need in order to calculate the absolute area between f(x) = sin x and the x-axis on ?
Will the absolute area be positive or negative, and why? Will the signed area will be positive or negative, and why?
Suppose f is positive on (−∞, −1] and [2,∞) and negative on the interval [−1, 2]. Write (a) the signed area and (b) the absolute area between the graph of f and the x-axis on [−3, 4] in terms of definite integrals that do not involve absolute values.
Find the sum or quantity without completely expanding or calculating any sums.
Givenand, find the value of.
Repeat Exercise 13 for the function f shown above at the right, on the interval
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