In Problems 69–72, the left sum L n or the right sum R n is used to approximate the definite integral to the indicated accuracy. How large must n be chosen in each case? ( Each function is increasing over the indicated interval .) 70. ∫ 0 10 ln ( x 2 + 1 ) d x = L n ± 0.5
In Problems 69–72, the left sum L n or the right sum R n is used to approximate the definite integral to the indicated accuracy. How large must n be chosen in each case? ( Each function is increasing over the indicated interval .) 70. ∫ 0 10 ln ( x 2 + 1 ) d x = L n ± 0.5
Solution Summary: The author explains how to find the value of n such that the left sum L_n approximates the given definite integral.
In Problems 69–72, the left sum Ln or the right sum Rn is used to approximate the definite integral to the indicated accuracy. How large must n be chosen in each case? (Each function is increasing over the indicated interval.)
70.
∫
0
10
ln
(
x
2
+
1
)
d
x
=
L
n
±
0.5
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
3.
An animal population is increasing at a rate of 31 +36t per year (where t is
measured in years). By how much does the animal population increase between the
fourth and tenth years?
Chapter 5 Solutions
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