Problems 39–66 are mixed—some may require use of the integration -by-parts formula along with techniques we have considered earlier; others may require repeated use of the integration-by-parts formula. Assume that g ( x ) > 0 whenever ln g ( x ) is involved. 49. ∫ x ln ( 1 + x 2 ) d x
Problems 39–66 are mixed—some may require use of the integration -by-parts formula along with techniques we have considered earlier; others may require repeated use of the integration-by-parts formula. Assume that g ( x ) > 0 whenever ln g ( x ) is involved. 49. ∫ x ln ( 1 + x 2 ) d x
Solution Summary: The author calculates the value of indefinite integral displaystyle, int xmathrmln(1+
Problems 39–66 are mixed—some may require use of the integration-by-parts formula along with techniques we have considered earlier; others may require repeated use of the integration-by-parts formula. Assume that g (x) > 0 whenever ln g(x) is involved.
49.
∫
x
ln
(
1
+
x
2
)
d
x
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.
For each dif erential equation in Problems 1–21, find the general solutionby finding the homogeneous solution and a particular solution.
Please DO NOT YOU THE PI method where 1/f(r) * x. Dont do that.
Instead do this, assume for yp = to something, do the 1 and 2 derivative of it and then plug it in the equation to find the answer.
Suppose a person's utility function for items x and y is u = ln(x) + ln(y), and he currently has $200 in his pocket, and the price of x is $10 per item and the price of y is $20 per item, find the combination that maximises his utility.
Solve.
a) ln(x+1) + ln(x-1) = 0
b) e8-5x = 16
c) ln(2x) - ln4 = 3
d) 2ln(x+3) = ln(12x)
Chapter 6 Solutions
Pearson eText for Calculus for Business, Economics, Life Sciences, and Social Sciences, Brief Version -- Instant Access (Pearson+)
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