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Chapter 4: Q. 9 (page 403)
The function,
is continuous and differentiable on the interval ____ .
The function is continuous and differentiable on the interval .
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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 21–62. 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: ).
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.
Explain why at this point we don’t have an integration formula for the function whereas we do have an integration formula for .
Given a simple proof that if n is a positive integer and c is any real number, then
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