(a) Sketch the graph of the function on the given interval. Illustrate the midpoint Riemann sum by sketching the appropriate rectangles. Calculate the midpoint Riemann sum for n=4, being sure to show all work. Use a calculator to calculate the left Riemann sum for n=64. f(x)= 1-x^2 on [0,2] ; n=4

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Show all work, thank you! 
Not sure if my calculator got the right answer, so  wanted to double check that as well. Can use a TI-84 plus calculator. 

(a) Sketch the graph of the function on
the given interval. Illustrate the
midpoint Riemann sum by sketching
the appropriate rectangles. Calculate
the midpoint Riemann sum for n=4,
being sure to show all work. Use a
calculator to calculate the left
Riemann sum for n=64. f(x)= 1-x^2 on
[0,2] ; n=4
(b) For the previous function on the
given interval, calculate the definite
integral using the infinite limit of the
Right Riemann Sum.
Transcribed Image Text:(a) Sketch the graph of the function on the given interval. Illustrate the midpoint Riemann sum by sketching the appropriate rectangles. Calculate the midpoint Riemann sum for n=4, being sure to show all work. Use a calculator to calculate the left Riemann sum for n=64. f(x)= 1-x^2 on [0,2] ; n=4 (b) For the previous function on the given interval, calculate the definite integral using the infinite limit of the Right Riemann Sum.
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