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Numerade Educator

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Problem 43 Easy Difficulty

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

$ y = \tan^2 x $ , $ y = \sqrt{x} $

Answer

0.25142

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Video Transcript

we want to find the area of the enclosed region by these two functions. The 1st 1 in blue is why equals 10 X squared. And the 2nd 1 in green is why equals discreet of X. So using a graphing calculator we see, actually that there are many regions in fact are infinitely many regions. Oh, okay. And we see that they're in fact increasing in size. So if we were to try to increase, if we were to try toe out of all of these areas, it wouldn't even converge to a real number since we're adding numbers which are increasing in size. So instead what we're going to do is we're just going to zoom up on this first region here, and we're going to determine the area of this region. So let's do that. The area, as usual, we're going to be doing an integral area is equal to integral. We see that our points of intersection are X equals zero and X equals 0.749 We're going to do the top function minus the bottom function so screwed X minus 10 squared X dx. Now, where lot using graphic. We're allowed to use a calculator for this question. So plugging this into a calculator and rounding to five decimals gives us our answer of 0.2514 two as the area of the enclosed region.