Chapter 11: Problem 14
Find the indefinite integral and check your result by differentiation. $$ \int 4 y^{-3} d y $$
Chapter 11: Problem 14
Find the indefinite integral and check your result by differentiation. $$ \int 4 y^{-3} d y $$
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Get started for freeTwo 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? $$ R_{1}=7.21+0.26 t+0.02 t^{2}, R_{2}=7.21+0.1 t+0.01 t^{2} $$
Use the Midpoint Rule with \(n=4\) to approximate the area of the region. Compare your result with the exact area obtained with a definite integral. $$ f(y)=4 y-y^{2}, \quad[0,4] $$
Use a computer or programmable calculator to approximate the definite integral using the Midpoint Rule and the Trapezoidal Rule for \(n=4\), \(8,12,16\), and 20. $$ \int_{0}^{4} \sqrt{2+3 x^{2}} d x $$
Use 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.) $$ f(x)=x\left(x^{2}-3 x+3\right), g(x)=x^{2} $$
The revenue from a manufacturing process (in millions of dollars per year) is projected to follow the model \(R=100\) for 10 years. Over the same period of time, the cost (in millions of dollars per year) is projected to follow the model \(C=60+0.2 t^{2}\), where \(t\) is the time (in years). Approximate the profit over the 10 -year period.
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