One extremely useful result of multivariable calculus, often applied to statistics as well as physics and engineering, is the computation of the area under the bell-curve: 1= [² & I -x² e dx There is no elementary antiderivative of e-x². However, we can side-step this problem by using a very clever double integral as follows. a) Sketch y = e-x² b) Show the following: P-[[²²-42d5 c) Convert the double integral for 1² to polar coordinates and evaluate. d) Conclude that I = - √ and admire the beauty of math. = dx dy

One extremely useful result of multivariable calculus, often applied to statistics as well as physics and engineering, is the computation of the area under the bell-curve: 1= [² & I -x² e dx There is no elementary antiderivative of e-x². However, we can side-step this problem by using a very clever double integral as follows. a) Sketch y = e-x² b) Show the following: P-[[²²-42d5 c) Convert the double integral for 1² to polar coordinates and evaluate. d) Conclude that I = - √ and admire the beauty of math. = dx dy

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter2: Graphical And Tabular Analysis

Section2.1: Tables And Trends

Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...

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