Exam 5: Integration and Its Applications

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Use the Midpoint Rule with n = 4 to approximate the area of the region bounded by the graph of Use the Midpoint Rule with n = 4 to approximate the area of the region bounded by the graph of   and the x-axis over the interval   Round your answer to 4 decimal places. ​ and the x-axis over the interval Use the Midpoint Rule with n = 4 to approximate the area of the region bounded by the graph of   and the x-axis over the interval   Round your answer to 4 decimal places. ​ Round your answer to 4 decimal places. ​

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Use any basic integration formula or formulas to find the indefinite integral Use any basic integration formula or formulas to find the indefinite integral   ​

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Evaluate the integral Evaluate the integral   ​

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The graph of the derivative of a function is given below.Sketch the graphs of two functions that have the given derivative. ​ The graph of the derivative of a function is given below.Sketch the graphs of two functions that have the given derivative. ​   ​

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The demand function for a product is The demand function for a product is   ,where p is the number of dollars and x is the number of units.If the equilibrium price is $20,what is the consumer's surplus? ​ ,where p is the number of dollars and x is the number of units.If the equilibrium price is $20,what is the consumer's surplus? ​

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Determine the graph whose area (the shaded region)is represented by the integral. ​ Determine the graph whose area (the shaded region)is represented by the integral. ​   ​

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Find the area between the curve Find the area between the curve   and the x-axis from   to   ​ and the x-axis from Find the area between the curve   and the x-axis from   to   ​ to Find the area between the curve   and the x-axis from   to   ​

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Set up the definite integral that gives the area of the region bounded by the graphs. ​ Set up the definite integral that gives the area of the region bounded by the graphs. ​     ​   ​ Set up the definite integral that gives the area of the region bounded by the graphs. ​     ​   ​Set up the definite integral that gives the area of the region bounded by the graphs. ​     ​   ​

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