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Graph the region between the curves and use your calculator to compute the area correct to five decimal places.$y = \frac{2}{1 + x^4}$ , $y = x^2$

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Heather Z.

Oregon State University

Kayleah T.

Harvey Mudd College

Kristen K.

University of Michigan - Ann Arbor

Michael J.

Idaho State University

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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

University of Toronto
Heather Z.

Oregon State University

Kayleah T.

Harvey Mudd College

Kristen K.

University of Michigan - Ann Arbor

Michael J.

Idaho State University

Lectures

Join Bootcamp