Chapter 11: Problem 28
Find the indefinite integral and check your result by differentiation. $$ \int(5-x) d x $$
Chapter 11: Problem 28
Find the indefinite integral and check your result by differentiation. $$ \int(5-x) d x $$
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Get started for freeUse a graphing utility to graph the region bounded by the graphs of the functions. Write the definite integrals that represent the area of the region. (Hint: Multiple integrals may be necessary.) $$ f(x)=2 x, g(x)=4-2 x, h(x)=0 $$
Use the Midpoint Rule with \(n=4\) to approximate the area of the region bounded by the graph of \(f\) and the \(x\) -axis over the interval. Compare your result with the exact area. Sketch the region. $$ f(x)=4-x^{2} $$ $$ [0,2] $$
You are given the rate of investment \(d l / d t\). Find the capital accumulation over a five-year period by evaluating the definite integral Capital accumulation \(=\int_{0}^{5} \frac{d l}{d t} d t\) where \(t\) is the time in years. $$ \frac{d I}{d t}=\frac{12,000 t}{\left(t^{2}+2\right)^{2}} $$
Find the change in cost \(C\), revenue \(R\), or profit \(P\), for the given marginal. In each case, assume that the number of units \(x\) increases by 3 from the specified value of \(x\). $$ \frac{d R}{d x}=48-3 x \quad x=12 $$
Two models, \(R_{1}\) and \(R_{2}\), are given for revenue (in billions of dollars per year) for a large corporation. Both models are estimates of revenues for 2007 through 2011, with \(t=7\) corresponding to \(2007 .\) Which model is projecting the greater revenue? How much more total revenue does that model project over the five-year period? $$ R_{1}=7.21+0.58 t, R_{2}=7.21+0.45 t $$
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