3Consider 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| (206x2) 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 sameintegral, except that the lower limit of integration has been changed).

Given the integral ∫032x-6x2dx

Answered: Consider the integral (2x – 6x²) dx (a)…

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?

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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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 this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus.

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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