Docsity
Docsity

Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity


Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan


Guidelines and tips
Guidelines and tips

Quiz 101 in MTH 121 - Area under the Curve of f(x) = √(1-x²) from 0 to 1 - Prof. Ron Banno, Quizzes of Analytical Geometry and Calculus

A quiz from essex county college's division of mathematics, focusing on finding the area under the curve of the function f(x) = √(1-x²) from x = 0 to x = 1. The quiz includes a graph of the function and asks students to find the area using both the method discussed in class and geometry.

Typology: Quizzes

Pre 2010

Uploaded on 08/08/2009

koofers-user-5ko-1
koofers-user-5ko-1 🇺🇸

10 documents

1 / 1

Related documents


Partial preview of the text

Download Quiz 101 in MTH 121 - Area under the Curve of f(x) = √(1-x²) from 0 to 1 - Prof. Ron Banno and more Quizzes Analytical Geometry and Calculus in PDF only on Docsity! MTH 121 — Summer — 2005 Essex County College — Division of Mathematics Quiz # 101 — Printed June 15, 2005 Name: Signature: Show all work clearly and in order, and box your final answers . Justify your answers alge- braically whenever possible. You have 20 minutes to take this 10 point quiz. When you do use your calculator, sketch all relevant graphs and write down all relevant mathematics. 1. Use the method discussed in class to find an expression for the area under the graph of f as a limit. f (x) = √ 1− x2, x = 0, x = 1, y = 0. In[2]:= Plot@Sqrt@1 - x^2D, 8x, 0, 1<, AspectRatio Ø AutomaticD 0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1 Out[2]= Ü Graphics Ü Untitled-1 1 Figure 1: Graph of f (x) = √ 1− x2 on the interval [0, 1]. Solution: ∫ 1 0 √ 1− x2 dx = lim n→∞  n∑ i=1  1 n · √ 1− ( i n )2  2. Use the graph and your knowledge of geometry to find this area.∫ 1 0 √ 1− x2 dx Solution: This is just a quarter of a unit circle.∫ 1 0 √ 1− x2 dx = 1 4 · π · 12 = π 4 1This document was prepared by Ron Bannon using LATEX2ε. 1
Docsity logo



Copyright © 2024 Ladybird Srl - Via Leonardo da Vinci 16, 10126, Torino, Italy - VAT 10816460017 - All rights reserved