Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Concept explainers

Riemann Sum
Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence t…
Riemann Integral
Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.
Question
3 Consider the integral (2x – 6x²) dx (a) Use right endpoints and n sub-intervals to find the formula for the n-rectangle Riemann Sum. What is the value of this sum when n = 12? (b) Evaluate the integral by finding the limit as n → ∞ of the expression you found in part (a). (c) If you were to compute the integral | (20 6x2) dx using Riemann sums and right endpoints, - what formula for the x; would you use? Do not evaluate the integral. (Note that this is the same integral, except that the lower limit of integration has been changed).
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Transcribed Image Text:3 Consider the integral (2x – 6x²) dx (a) Use right endpoints and n sub-intervals to find the formula for the n-rectangle Riemann Sum. What is the value of this sum when n = 12? (b) Evaluate the integral by finding the limit as n → ∞ of the expression you found in part (a). (c) If you were to compute the integral | (20 6x2) dx using Riemann sums and right endpoints, - what formula for the x; would you use? Do not evaluate the integral. (Note that this is the same integral, except that the lower limit of integration has been changed).
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