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Consider the integral given by (2²-32) dz (a) Find an approximation to this integral (1) by using a Riemann sum with right endpoints and n-8. Your answer should be correct to four decimal places. Approximation of (1): R -1.5 Parts (b) and (c) will continue to consider the given integral (1), along with the following definition of a definite integral: (2) where z, are right hand endpoints. Note that instead of approximating an integral (with, say, 8 rectangles, as above), this expression allows us to use a limit of a sum to evaluate an integral exactly. [1(e)dx= = lim (1) 3 f(zi)Az, (b) Determine the Ar and z, that would be required if we wanted to evaluate integral (1) using definition (2). Your answer might include some i or n

Consider the integral given by (2²-32) dz (a) Find an approximation to this integral (1) by using a Riemann sum with right endpoints and n-8. Your answer should be correct to four decimal places. Approximation of (1): R -1.5 Parts (b) and (c) will continue to consider the given integral (1), along with the following definition of a definite integral: (2) where z, are right hand endpoints. Note that instead of approximating an integral (with, say, 8 rectangles, as above), this expression allows us to use a limit of a sum to evaluate an integral exactly. [1(e)dx= = lim (1) 3 f(zi)Az, (b) Determine the Ar and z, that would be required if we wanted to evaluate integral (1) using definition (2). Your answer might include some i or n

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the integral given by (2²-32) dz (a) Find an approximation to this integral (1) by using a Riemann sum with right endpoints and n-8. Your answer should be correct to four decimal places. Approximation of (1): R -1.5 Parts (b) and (c) will continue to consider the given integral (1), along with the following definition of a definite integral: (2) where z, are right hand endpoints. Note that instead of approximating an integral (with, say, 8 rectangles, as above), this expression allows us to use a limit of a sum to evaluate an integral exactly. [1(e)dz = 3 = lim (1) f(zi)Az, (b) Determine the Az and z, that would be required if we wanted to evaluate integral (1) using definition (2). Your answer might include some i or n
Transcribed Image Text:Consider the integral given by (2²-32) dz (a) Find an approximation to this integral (1) by using a Riemann sum with right endpoints and n-8. Your answer should be correct to four decimal places. Approximation of (1): R -1.5 Parts (b) and (c) will continue to consider the given integral (1), along with the following definition of a definite integral: (2) where z, are right hand endpoints. Note that instead of approximating an integral (with, say, 8 rectangles, as above), this expression allows us to use a limit of a sum to evaluate an integral exactly. [1(e)dz = 3 = lim (1) f(zi)Az, (b) Determine the Az and z, that would be required if we wanted to evaluate integral (1) using definition (2). Your answer might include some i or n
f(a)dx= f(x)dz limf(xi)Az, fol where z, are right hand endpoints. Note that instead of approximating an integral (with, say, 8 rectangles, as above), this expression allows us to use a limit of a sum to evaluate an integral exactly. Ar= 0.5 (2) (b) Determine the Az and ar, that would be required if we wanted to evaluate integral (1) using definition (2). Your answer might include some i orn. # (c) Now, using the definition of an integral (2) and your answers for part (b), evaluate the specific integral you were given in by calculating it as a limit of a sum. You'll need to look up and use some known sum formulas (which you can find many places: try an internet search for sums of powers of integers, or check the online CLP text for this course.) Value of integral (1):
Transcribed Image Text:f(a)dx= f(x)dz limf(xi)Az, fol where z, are right hand endpoints. Note that instead of approximating an integral (with, say, 8 rectangles, as above), this expression allows us to use a limit of a sum to evaluate an integral exactly. Ar= 0.5 (2) (b) Determine the Az and ar, that would be required if we wanted to evaluate integral (1) using definition (2). Your answer might include some i orn. # (c) Now, using the definition of an integral (2) and your answers for part (b), evaluate the specific integral you were given in by calculating it as a limit of a sum. You'll need to look up and use some known sum formulas (which you can find many places: try an internet search for sums of powers of integers, or check the online CLP text for this course.) Value of integral (1):
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