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Repeat Exercise 47 for the curve $ y = (x^2 + 1)^{-1} - x^4 $.

Area below the given curve and above the $x$ -axis is $\approx 1.2326$

00:32

Frank L.

02:09

Gregory H.

Calculus 1 / AB

Chapter 5

Integrals

Section 4

Indefinite Integrals and the Net Change Theorem

Integration

Missouri State University

Harvey Mudd College

Boston College

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

04:58

Sketch the curve $ (x^2 + …

07:11

Use the guidelines of this…

11:07

17:51

01:57

Find the curvature $\kappa…

16:20

07:56

Use the method of Example …

17:18

16:30

00:43

Find the slope of the curv…

Alright based off of the problem, I'm trusting that are allowed to use a graphing calculator plus the equation is kind of awkward. X squared plus one to the negative first power. And then we have minus X. To the fourth hole account. I don't know how you would do this in your head and maybe there's some fancy math going on. But once you do that you can zoom in and we actually only care about the X coordinates. This must be an even function because it looks symmetric with the Y. Axis. And we care about negative .8692 positive .869. So that's what I'm gonna do. I'm gonna pull up my tool under my functions and sometimes you have to click around before you find where your integral is. Mhm. And I believe I typed that I remember that. So negative .8692 positive .869. Yeah. And uh you unfortunately I might have to re type this equation otherwise you can copy and paste it down. Um And then you also might want to tell the calculator that X. Is your independent variable. I'm sure some other calculators might do that for you. Um and I rounded these answers these bounds, so my answer might be off a little bit, but if I were rounding my answer I would write down 1.233. Rounding to three decim, otherwise you can copy down the whole thing. Um And it should make sense that that answer is correct because if you look at trying to zoom around and it's not letting me and alright, there we go. Uh That that looks about right, the area looks like it should be a little bit bigger than one but smaller than two. Um things like that. So 1.233 is what I would write down.

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In mathematics, precalculus is the study of functions (as opposed to calculu…

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Sketch the curve $ (x^2 + y^2)^3 = 4x^2y^2 $.

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Use the guidelines of this section to sketch the curve.

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Evaluate the definite integral.

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