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Chapter 11: Problem 17
Find the indefinite integral and check your result by differentiation. $$ \int e d t $$
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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. $$ f(x)=x(1-x)^{2} $$ $$ [0,1] $$
The integrand of the definite integral is a difference of two functions. Sketch the graph of each function and shade the region whose area is represented by the integral. $$ \int_{0}^{4}\left[(x+1)-\frac{1}{2} x\right] d x $$
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. $$ f(x)=1-x^{2}, \quad[-1,1] $$
Consumer Trends For the years 1996 through 2004 , the per capita consumption
of fresh pineapples (in pounds per year) in the United States can be modeled
by \(C(t)=\left\\{\begin{array}{c}-0.046 t^{2}+1.07 t-2.9,6 \leq t \leq 10 \\\
-0.164 t^{2}+4.53 t-26.8,10
The projected fuel cost \(C\) (in millions of dollars per year) for an airline company from 2007 through 2013 is \(C_{1}=568.5+7.15 t\), where \(t=7\) corresponds to \(2007 .\) If the company purchases more efficient airplane engines, fuel cost is expected to decrease and to follow the model \(C_{2}=525.6+6.43 t\). How much can the company save with the more efficient engines? Explain your reasoning.
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