SalasSV_08_07_ex - EXERCISES 8.7 ± c In Exercises 1–10,...

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Unformatted text preview: EXERCISES 8.7 ± c In Exercises 1–10, round your answers to four decimal places. 1. Estimate ± 12 x 2 dx by: (a) the left-endpoint estimate, n = 12; (b) the right-endpoint estimate n = 12; (c) the midpoint estimate, n = 6; (d) the trapezoidal rule, n = 12; (e) Simpson’s rule, n = 6. Check your results by performing the integration. 2. Estimate ± 1 sin 2 π x dx by: (a) the midpoint estimate, n = 3; (b) the trapezoidal rule, n = 6; (c) Simpson’s rule, n = 3. Check your results by performing the integration. 494 ± CHAPTER 8 TECHNIQUES OF INTEGRATION 3. Estimate ± 3 dx 1 + x 3 by: (a) the left-endpoint estimate, n = 6; (b) the right-endpoint estimate, n = 6; (c) the midpoint estimate, n = 3; (d) the trapezoidal rule, n = 6; (e) Simpson’s rule, n = 3. 4. Estimate ± π sin x π + x dx by: (a) the trapezoidal rule, n = 6; (b) Simpson’s rule, n = 3. 5. Find the approximate value of π by estimating the integral π 4 = tan − 1 1 = ± 1 dx 1 + x 2 by: (a) the trapezoidal rule, n = 4; (b) Simpson’s rule, n = 4. 6. Estimate ± 2 dx √ 4 + x 3 by: (a) the trapezoidal rule, n = 4; (b) Simpson’s rule, n = 2. 7. Estimate ± 1 − 1 cos ( x 2 ) dx by: (a) the midpoint estimate, n = 4; (b) the trapezoidal rule, n = 8; (c) Simpson’s rule, n = 4....
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This note was uploaded on 10/12/2010 for the course MATH 12345 taught by Professor Smith during the Spring '10 term at University of Houston - Downtown.

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SalasSV_08_07_ex - EXERCISES 8.7 ± c In Exercises 1–10,...

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