Exam 4: Section 2: Integration

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Use the properties of summation and Theorem 5.2 to evaluate the sum. Use the properties of summation and Theorem 5.2 to evaluate the sum.

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B

Find the limit. Find the limit.

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E

Use the properties of summation and Theorem 5.2 to evaluate the sum. Use the properties of summation and Theorem 5.2 to evaluate the sum.

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C

Find the sum given below. Find the sum given below.

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Use left endpoints and 10 rectangles to find the approximation of the area of the region between the graph of the function Use left endpoints and 10 rectangles to find the approximation of the area of the region between the graph of the function   and the x-axis over the interval   . Round your answer to the nearest integer. and the x-axis over the interval Use left endpoints and 10 rectangles to find the approximation of the area of the region between the graph of the function   and the x-axis over the interval   . Round your answer to the nearest integer. . Round your answer to the nearest integer.

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Use left endpoints and 12 rectangles to find the approximation of the area of the region between the graph of the function Use left endpoints and 12 rectangles to find the approximation of the area of the region between the graph of the function   and the x-axis over the interval   . Round your answer to four decimal places. and the x-axis over the interval Use left endpoints and 12 rectangles to find the approximation of the area of the region between the graph of the function   and the x-axis over the interval   . Round your answer to four decimal places. . Round your answer to four decimal places.

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Use sigma notation to write the sum Use sigma notation to write the sum   . .

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Find the sum given below. Find the sum given below.

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Use the properties of summation and Theorem 5.2 to evaluate the sum. Use the properties of summation and Theorem 5.2 to evaluate the sum.

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Use the limit process to find the area of the region between the graph of the function Use the limit process to find the area of the region between the graph of the function   and x-axis over the interval   . and x-axis over the interval Use the limit process to find the area of the region between the graph of the function   and x-axis over the interval   . .

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Use the properties of summation and Theorem 5.2 to evaluate the sum. Use the properties of summation and Theorem 5.2 to evaluate the sum.

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Use the summation formulas to rewrite the expression Use the summation formulas to rewrite the expression   without the summation notation. without the summation notation.

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The diagram below shows upper and lower sums for the function The diagram below shows upper and lower sums for the function   using 4 subintervals. Use upper and lower sums to approximate the area of the region using the 4 subintervals.  using 4 subintervals. Use upper and lower sums to approximate the area of the region using the 4 subintervals. The diagram below shows upper and lower sums for the function   using 4 subintervals. Use upper and lower sums to approximate the area of the region using the 4 subintervals.

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Use the properties of summation and Theorem 5.2 to evaluate the sum. Use the properties of summation and Theorem 5.2 to evaluate the sum.

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Find the limit of Find the limit of   as   .  as Find the limit of   as   .  . Find the limit of   as   .

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Find the limit of Find the limit of   as   .  as Find the limit of   as   .  . Find the limit of   as   .

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Find the sum given below. Find the sum given below.

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