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Calculating Riemann Sums and Integrals

Learn how to find Riemann sums and approximate integrals using the Midpoint Rule with sample points as midpoints. Evaluate integrals, interpret in terms of areas, and express as single integrals. Test your understanding through various problem-solving scenarios.

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Calculating Riemann Sums and Integrals

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  1. If {image} find the Riemann sum with n = 5 correct to 3 decimal places, taking the sample points to be midpoints. • -6.789816 • -25.856759 • -51.713519

  2. Use the Midpoint Rule with n = 10 to approximate the integral. {image} Select the correct answer. The choices are rounded to 3 decimal places • 66.969 • 669.685 • 23.032

  3. 1. 2. 3. Express the integral as a limit of sums. Then evaluate the limit. {image} • {image} • {image} • {image}

  4. 1. 2. 3. Evaluate the integral by interpreting it in terms of areas. {image} • {image} • {image} • {image}

  5. Evaluate the integral by interpreting it in terms of areas. {image} • -12 • 12 • 13

  6. 1. 2. 3. Express the sum as a single integral in the form {image} {image} • {image} • {image} • {image}

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