Exam 4: Section 4: Integration

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Find Find   given   . given Find   given   . .

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Find Find   given   . given Find   given   . .

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Evaluate the definite integral Evaluate the definite integral   . Use a graphing utility to verify your results. . Use a graphing utility to verify your results.

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Find the average value of Find the average value of   on the interval   . on the interval Find the average value of   on the interval   . .

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Determine the area of the given region. Determine the area of the given region.    Determine the area of the given region.

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Evaluate the definite integral of the algebraic function. Evaluate the definite integral of the algebraic function.   Use a graphing utility to verify your results. Use a graphing utility to verify your results.

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Evaluate the definite integral of the algebraic function. Evaluate the definite integral of the algebraic function.   Use a graphing utility to verify your results. Use a graphing utility to verify your results.

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Find the area of the region bounded by the graphs of the equations Find the area of the region bounded by the graphs of the equations   . Round your answer to the nearest whole number. . Round your answer to the nearest whole number.

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Evaluate the definite integral of the function. Evaluate the definite integral of the function.   Use a graphing utility to verify your results. Use a graphing utility to verify your results.

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Evaluate the definite integral of the algebraic function. Evaluate the definite integral of the algebraic function.   Use a graphing utility to verify your results. Use a graphing utility to verify your results.

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Evaluate the definite integral of a function Evaluate the definite integral of a function   . Use a graphing utility to verify your results. . Use a graphing utility to verify your results.

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The volume The volume   in liters of air in the lungs during a five-second respiratory cycle is approximated by the model   where   is the time in seconds. Approximate the average volume of air in the lungs during one cycle. Round your answer to four decimal places. in liters of air in the lungs during a five-second respiratory cycle is approximated by the model The volume   in liters of air in the lungs during a five-second respiratory cycle is approximated by the model   where   is the time in seconds. Approximate the average volume of air in the lungs during one cycle. Round your answer to four decimal places. where The volume   in liters of air in the lungs during a five-second respiratory cycle is approximated by the model   where   is the time in seconds. Approximate the average volume of air in the lungs during one cycle. Round your answer to four decimal places. is the time in seconds. Approximate the average volume of air in the lungs during one cycle. Round your answer to four decimal places.

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Find the average value of the function Find the average value of the function   over the interval   . over the interval Find the average value of the function   over the interval   . .

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The force The force   (in newtons) of a hydraulic cylinder in a press is proportional to the square of   where   is the distance (in meters) that the cylinder is extended in its cycle. The domain of   is   and   . Find the average force exerted by the press over the interval   . Round your answer to the nearest whole number. (in newtons) of a hydraulic cylinder in a press is proportional to the square of The force   (in newtons) of a hydraulic cylinder in a press is proportional to the square of   where   is the distance (in meters) that the cylinder is extended in its cycle. The domain of   is   and   . Find the average force exerted by the press over the interval   . Round your answer to the nearest whole number. where The force   (in newtons) of a hydraulic cylinder in a press is proportional to the square of   where   is the distance (in meters) that the cylinder is extended in its cycle. The domain of   is   and   . Find the average force exerted by the press over the interval   . Round your answer to the nearest whole number. is the distance (in meters) that the cylinder is extended in its cycle. The domain of The force   (in newtons) of a hydraulic cylinder in a press is proportional to the square of   where   is the distance (in meters) that the cylinder is extended in its cycle. The domain of   is   and   . Find the average force exerted by the press over the interval   . Round your answer to the nearest whole number. is The force   (in newtons) of a hydraulic cylinder in a press is proportional to the square of   where   is the distance (in meters) that the cylinder is extended in its cycle. The domain of   is   and   . Find the average force exerted by the press over the interval   . Round your answer to the nearest whole number. and The force   (in newtons) of a hydraulic cylinder in a press is proportional to the square of   where   is the distance (in meters) that the cylinder is extended in its cycle. The domain of   is   and   . Find the average force exerted by the press over the interval   . Round your answer to the nearest whole number. . Find the average force exerted by the press over the interval The force   (in newtons) of a hydraulic cylinder in a press is proportional to the square of   where   is the distance (in meters) that the cylinder is extended in its cycle. The domain of   is   and   . Find the average force exerted by the press over the interval   . Round your answer to the nearest whole number. . Round your answer to the nearest whole number.

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Determine the area of the given region. Determine the area of the given region.    Determine the area of the given region.

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The force The force   (in newtons) of a hydraulic cylinder in a press is proportional to the square of   where   is the distance (in meters) that the cylinder is extended in its cycle. The domain of   is   and   . Find   as a function of   . (in newtons) of a hydraulic cylinder in a press is proportional to the square of The force   (in newtons) of a hydraulic cylinder in a press is proportional to the square of   where   is the distance (in meters) that the cylinder is extended in its cycle. The domain of   is   and   . Find   as a function of   . where The force   (in newtons) of a hydraulic cylinder in a press is proportional to the square of   where   is the distance (in meters) that the cylinder is extended in its cycle. The domain of   is   and   . Find   as a function of   . is the distance (in meters) that the cylinder is extended in its cycle. The domain of The force   (in newtons) of a hydraulic cylinder in a press is proportional to the square of   where   is the distance (in meters) that the cylinder is extended in its cycle. The domain of   is   and   . Find   as a function of   . is The force   (in newtons) of a hydraulic cylinder in a press is proportional to the square of   where   is the distance (in meters) that the cylinder is extended in its cycle. The domain of   is   and   . Find   as a function of   . and The force   (in newtons) of a hydraulic cylinder in a press is proportional to the square of   where   is the distance (in meters) that the cylinder is extended in its cycle. The domain of   is   and   . Find   as a function of   . . Find The force   (in newtons) of a hydraulic cylinder in a press is proportional to the square of   where   is the distance (in meters) that the cylinder is extended in its cycle. The domain of   is   and   . Find   as a function of   . as a function of The force   (in newtons) of a hydraulic cylinder in a press is proportional to the square of   where   is the distance (in meters) that the cylinder is extended in its cycle. The domain of   is   and   . Find   as a function of   . .

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Evaluate the definite integral of the trig function. Evaluate the definite integral of the trig function.   Use a graphing utility to verify your results. Use a graphing utility to verify your results.

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Evaluate the definite integral of the algebraic function. Evaluate the definite integral of the algebraic function.   Use a graphing utility to verify your results. Use a graphing utility to verify your results.

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