Exam 4: Section 5: Integration

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Find the indefinite integral Find the indefinite integral   . .

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Find the indefinite integral Find the indefinite integral   . .

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Find the indefinite integral of the following function. Find the indefinite integral of the following function.

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The rate of disbursement The rate of disbursement   of a 2 million dollar federal grant is proportional to the square of   Time t is measured in days   and   is the amount that remains to be disbursed. Find the amount that remains to be disbursed after 30 days. Assume that all the money will be disbursed in 100 days. of a 2 million dollar federal grant is proportional to the square of The rate of disbursement   of a 2 million dollar federal grant is proportional to the square of   Time t is measured in days   and   is the amount that remains to be disbursed. Find the amount that remains to be disbursed after 30 days. Assume that all the money will be disbursed in 100 days. Time t is measured in days The rate of disbursement   of a 2 million dollar federal grant is proportional to the square of   Time t is measured in days   and   is the amount that remains to be disbursed. Find the amount that remains to be disbursed after 30 days. Assume that all the money will be disbursed in 100 days. and The rate of disbursement   of a 2 million dollar federal grant is proportional to the square of   Time t is measured in days   and   is the amount that remains to be disbursed. Find the amount that remains to be disbursed after 30 days. Assume that all the money will be disbursed in 100 days. is the amount that remains to be disbursed. Find the amount that remains to be disbursed after 30 days. Assume that all the money will be disbursed in 100 days.

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Find the indefinite integral of the following function and check the result by differentiation. Find the indefinite integral of the following function and check the result by differentiation.

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The sales S (in thousands of units) of a seasonal product are given by the model The sales S (in thousands of units) of a seasonal product are given by the model   where t is the time in months, with   corresponding to January. Find the average sales for the first quarter   . Round your answer to three decimal places. where t is the time in months, with The sales S (in thousands of units) of a seasonal product are given by the model   where t is the time in months, with   corresponding to January. Find the average sales for the first quarter   . Round your answer to three decimal places. corresponding to January. Find the average sales for the first quarter The sales S (in thousands of units) of a seasonal product are given by the model   where t is the time in months, with   corresponding to January. Find the average sales for the first quarter   . Round your answer to three decimal places. . Round your answer to three decimal places.

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Evaluate the definite integral. Evaluate the definite integral.

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Find the indefinite integral of the following function and check the result by differentiation. Find the indefinite integral of the following function and check the result by differentiation.

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Solve the differential equation. Solve the differential equation.

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Find the indefinite integral Find the indefinite integral   . .

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The rate of depreciation The rate of depreciation   of a machine is inversely proportional to the square of   where V is the value of the machine t years after it was purchased. The initial value of the machine was   and its value decreased   in the first year. Estimate its value after 6 years. Round your answer to the nearest integer. of a machine is inversely proportional to the square of The rate of depreciation   of a machine is inversely proportional to the square of   where V is the value of the machine t years after it was purchased. The initial value of the machine was   and its value decreased   in the first year. Estimate its value after 6 years. Round your answer to the nearest integer. where V is the value of the machine t years after it was purchased. The initial value of the machine was The rate of depreciation   of a machine is inversely proportional to the square of   where V is the value of the machine t years after it was purchased. The initial value of the machine was   and its value decreased   in the first year. Estimate its value after 6 years. Round your answer to the nearest integer. and its value decreased The rate of depreciation   of a machine is inversely proportional to the square of   where V is the value of the machine t years after it was purchased. The initial value of the machine was   and its value decreased   in the first year. Estimate its value after 6 years. Round your answer to the nearest integer. in the first year. Estimate its value after 6 years. Round your answer to the nearest integer.

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Find the following indefinite integral. Find the following indefinite integral.

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Find an equation for the function Find an equation for the function   whose derivative is   and whose graph passes through the point   . whose derivative is Find an equation for the function   whose derivative is   and whose graph passes through the point   . and whose graph passes through the point Find an equation for the function   whose derivative is   and whose graph passes through the point   . .

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Find the indefinite integral Find the indefinite integral

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Find the indefinite integral. Find the indefinite integral.

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Evaluate the definite integral. Evaluate the definite integral.

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Evaluate the following definite integral. Evaluate the following definite integral.   Use a graphing utility to check your answer. Use a graphing utility to check your answer.

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The oscillating current in an electrical circuit is The oscillating current in an electrical circuit is   where I is measured in amperes and t is measured in seconds. Find the average current for the time interval   . Round your answer to three decimal places. where I is measured in amperes and t is measured in seconds. Find the average current for the time interval The oscillating current in an electrical circuit is   where I is measured in amperes and t is measured in seconds. Find the average current for the time interval   . Round your answer to three decimal places. . Round your answer to three decimal places.

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Find the indefinite integral. Find the indefinite integral.

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Solve the differential equation. Solve the differential equation.

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