Problem

Graph the region between the curves and use your …

01:24

Problem 41 Easy Difficulty

Graph the region between the curves and use your calculator to compute the area correct to five decimal places.

$ y = \frac{2}{1 + x^4} $ , $ y = x^2 $

Answer

2.80123

Topics

Applications of Integration

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 6

Applications of Integration

Section 1

Areas Between Curves

Discussion

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Problem 41

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Video Transcript

we want to find the area of the region enclosed by these two functions. The 1st 1 in blue is Y equals two over one plus X to the fore. And the 2nd 1 in green is y equals X squared. Using a graphing calculator, we get the following graph and we see that we want to determine the area of this region here. We also find that the points of intersection okay, X equals minus one and X equals one s o. What we want to do is integrate from minus 1 to 1. So area equals into go from minus one toe, one of our top function minus or bottom function. Here, the top function is the blue one, and the bottom function is the green one. And, um, this this first part is a little complicated to solve. Of course, we we could do the integral of X squared. Uh, but we're allowed to use our calculator for this Integral. So plugging this into a calculator gives us the approximate area, which is 2.8 012 three. Uh recalled that the question only asks for five decimal places

Kenneth K.

University of Toronto

Topics

Applications of Integration

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 6

Applications of Integration

Section 1

Areas Between Curves

Top Calculus 2 / BC Educators

Heather Z.

Oregon State University

Kayleah T.

Harvey Mudd College

Kristen K.

University of Michigan - Ann Arbor

Michael J.

Idaho State University