Exam 5: Integrals

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Evaluate the definite integral. Evaluate the definite integral.

(Short Answer)
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Approximate the area under the curve Approximate the area under the curve   from 1 to 2 using ten approximating rectangles of equal widths and right endpoints.Round theAnswer to the nearest hundredth. from 1 to 2 using ten approximating rectangles of equal widths and right endpoints.Round theAnswer to the nearest hundredth.

(Essay)
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Evaluate the integral if it exists. Evaluate the integral if it exists.

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Select the correct Answer: for each question. -Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. Select the correct Answer: for each question. -Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.

(Multiple Choice)
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Find the indefinite integral.Select the correct Answer Find the indefinite integral.Select the correct Answer

(Multiple Choice)
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Select the correct Answer for each question. -Find the indefinite integral. Select the correct Answer for each question. -Find the indefinite integral.

(Multiple Choice)
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Find the area of the region under the graph of Find the area of the region under the graph of   on [a, b].  on [a, b]. Find the area of the region under the graph of   on [a, b].

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Find the integral. Find the integral.

(Essay)
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Evaluate the integral if it exists. Evaluate the integral if it exists.

(Essay)
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Show that Show that   by interpreting the definite integral geometrically. by interpreting the definite integral geometrically.

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Select the correct Answer: for each question. -Evaluate Select the correct Answer: for each question. -Evaluate

(Multiple Choice)
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Select the correct Answer for each question. -Evaluate the integral. Select the correct Answer for each question. -Evaluate the integral.

(Multiple Choice)
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Evaluate the limit after first finding the sum Evaluate the limit after first finding the sum   using the summation formulas.  using the summation formulas. Evaluate the limit after first finding the sum   using the summation formulas.

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Find the limit. Find the limit.

(Short Answer)
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Evaluate the integral.Select the correct Answer Evaluate the integral.Select the correct Answer

(Multiple Choice)
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An animal population is increasing at a rate of An animal population is increasing at a rate of   per year (where   is measured in years).By how much does the animal population increase between the fourth and tenth years? per year (where An animal population is increasing at a rate of   per year (where   is measured in years).By how much does the animal population increase between the fourth and tenth years? is measured in years).By how much does the animal population increase between the fourth and tenth years?

(Essay)
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Select the correct Answer for each question. -Evaluate the integral by making the given substitution. Select the correct Answer for each question. -Evaluate the integral by making the given substitution.

(Multiple Choice)
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Evaluate the integral by making the given substitution. Evaluate the integral by making the given substitution.

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Evaluate the integral.Select the correct Answer Evaluate the integral.Select the correct Answer

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Select the correct Answer for each question. -Find the integral. Select the correct Answer for each question. -Find the integral.

(Multiple Choice)
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