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Quiz 2 for Math 106: Calculus - Approximation and Area, Exercises of Calculus

Aliah UniversityCalculus

The second quiz for math 106, a calculus course. The quiz covers topics on approximation using left sums and finding the area between two functions. Students are required to determine the number of subdivisions needed for a left sum approximation with a given error bound and find the area of the region between two functions.

Typology: Exercises

2012/2013

Uploaded on 03/16/2013

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Math 106 Name
Quiz 2
9/21/12
Read directions carefully and show your work. Partial credit will be assigned based upon the correctness,
completeness, and clarity of your answers.
1. Let I=Zπ/2
0
xsin x dx. How many subdivisions are required to obtain a left sum approximation with
error of at most 1/10,000? Recall that the error bound estimates for left sums may be determined using:
|I−Ln| ≤ K1(b−a)2
2n.
2. Find the area of the region between y= 2x2and
y=x4−2x2.
1

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Download Quiz 2 for Math 106: Calculus - Approximation and Area and more Exercises Calculus in PDF only on Docsity!

Math 106 Name Quiz 2 9/21/

Read directions carefully and show your work. Partial credit will be assigned based upon the correctness, completeness, and clarity of your answers.

  1. Let I =

∫ (^) π/ 2

0

x sin x dx. How many subdivisions are required to obtain a left sum approximation with error of at most 1/10,000? Recall that the error bound estimates for left sums may be determined using:

|I − Ln| ≤

K 1 (b − a)^2 2 n

  1. Find the area of the region between y = 2x^2 and y = x^4 − 2 x^2.