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

$ y = e^{1 - x^2} $ , $ y = x^4 $

3.66016

Applications of Integration

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Baylor University

University of Michigan - Ann Arbor

Idaho State University

we want to determine the area of the enclosed region by these two functions. The first function is in blue. It's y equals E to the one minus X squared. And the second function isn't green. Why equals X to the fore? Using a graphing calculator, we see that the enclosed region is this shape over here and we want to determine its area. So we're going to do an integral area is equal to integral. So the graphing calculator shows us our points of intersection. The left most point of intersection happens at X equals minus one, and the right point of intersection happens at X equals one. So we're going to integrate from left to right minus 1 to 1. We're going to integrate our top function minus our bottom function. The top function is in blue, so e to the one minus X squared. And our second bottom function is in green X to the fore D X computing. This integral manually is not very easy because of this exponential part here, however, we are allowed to use and integral calculator where any calculator that consult into girls So plugging this into our calculator gives us the approximate value of the area 3.6601 six as the area of the enclosed region