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Chapter 4: Q. 34 (page 325)
Write out each sum in Exercises 34 in expanded form, and then calculate the value of the sum.
The expanded notation is and their sum is .
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Explain why we call the collection of antiderivatives of a function f a family. How are the antiderivatives of a function related?
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?
Write each expression in Exercises 41鈥�43 in one sigma notation (with some extra terms added to or subtracted from the sum, as necessary).
Show by exhibiting a counterexample that, in general, . In other words, find two functions f and g such that the integral of their quotient is not equal to the quotient of their integrals.
Calculate the exact value of each definite integral in Exercises 47鈥�52 by using properties of definite integrals and the formulas in Theorem 4.13.
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