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Chapter 4: Q. 7 (page 404)
Riemann sums: Calculate each of the following Riemann sum
approximations for the definite integral of f on [a, b], using the
given value of n.
The left sum for on ,.
The value is.
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Find the sum or quantity without completely expanding or calculating any sums.
Given and,. Find the value of.
Use integration formulas to solve each integral in Exercises 21鈥�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 .
As n approaches infinity this sequence of partial sums could either converge meaning that the terms eventually approach some finite limit or it could diverge to infinity meaning that the terms eventually grow without bound. which do you think is the case here and why?
Consider the region between f and g on [0, 4] as in the
graph next at the left. (a) Draw the rectangles of the left-
sum approximation for the area of this region, with n = 8.
Then (b) express the area of the region with definite
integrals that do not involve absolute values.
Use integration formulas to solve each integral in Exercises 21鈥�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 .
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