calculus 2 1. Create a thread to answer the following questions.• In your own words and using appropriate figures, describe the methods of upper sums and lower sums in approximating the area of a region.• A function is continuous, nonnegative, concave upward, and decreasing on the interval [0, a]. Does using the right endpoints of the subintervals produce an overestimate or an underestimate of the area of the region bounded by the function and the x-axis? Justify youranswer.

Using lower Riemann sum the area under the curve bounded by the curve in [a, b] using n partitions…

Answered: Create a thread to answer the following…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Question

100%

calculus 2

1. Create a thread to answer the following questions.
• In your own words and using appropriate figures, describe the methods of upper sums and lower sums in approximating the area of a region.
• A function is continuous, nonnegative, concave upward, and decreasing on the interval [0, a]. Does using the right endpoints of the subintervals produce an overestimate or an underestimate of the area of the region bounded by the function and the x-axis? Justify your
answer.

Expert Solution

Step 1: Information

Using lower Riemann sum the area under the curve bounded by the curve $y equals f left parenthesis x right parenthesis$ in [a, b] using n partitions of the interval is given by

$A subscript L equals sum from i equals 0 to n minus 1 of space f open parentheses x subscript i close parentheses space increment x subscript i h e r e space increment x subscript i space i s space t h e space w i d t h space o f space t h e space i t h space p a r t i t i o n.$

In lower Riemann sum we take hight of the rectangle at left end point of the partition.

Similarly using upper Riemann sum the area under the curve bounded by the curve $y equals f left parenthesis x right parenthesis$ in [a, b] using n partitions of the interval is given by

$A subscript R equals sum from i equals 0 to n minus 1 of space f open parentheses x subscript i close parentheses space increment x subscript i$

In upper Riemann sum we take hight of the rectangle at right end point of the partition.