💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!



Numerade Educator



Problem 6 Easy Difficulty

(a) Set up an integral for the area of the surface obtained by rotating the curve about (i) the x-axis and (ii) the y-axis.
(b) Use the numerical integration capability of a calculator to evaluate the surface areas correct to four decimal places.

$ y = \tan^{-1} x $ , $ 0 \le x \le 2 $


a)(i) $$\quad S_{x}=\int_{0}^{2} 2 \pi \arctan x \sqrt{1+\left(\frac{1}{1+x^{2}}\right)^{2}} d x$$
(ii) $$\quad S_{y}=\int_{0}^{2} 2 \pi x \sqrt{1+\left(\frac{1}{1+x^{2}}\right)^{2}} d x$$
b) (i) $$9.7956$$
(ii) $$13.7209$$


You must be signed in to discuss.

Video Transcript

So you have have dysfunction. Why she called Thio Inverse tangent. Dodge intelligent itiveness affects or, uh, pungent clecs, if you will come down. Yeah. Here. Uh, X with y axis. All these looks sort of like the, um can you do rotate dysfunction? What is the day? Surface of evolution over there are invisible. The x axis from Syria to So we did that. Moving on pain shaped like these. So, like some sort of come, but with the spill, if you try to maybe stand up because it has this pointy base eso to the area for these area for the service of revolution, I's gonna be Yeah, well, they drove from 0 to 2. Do off effects. Cam's square with the one plus their development function squared. Yes, that comes to buy this'll piece here is yes, the next day. Differential Wolf. The length of the curve from them. This would be because for me, Parker, rule the conference. This she discovered. Ah. So these would be We're taking about X, and if you want to update about why, But we have our was seen good. Not taking about why we're gonna have these. It's curved from zero to She wrote to for X when they were taking about Why, while this is there, the y axis the surface would look something like, Yes, until what would be shaped? Uh, yeah. So, God, bathroom on the the area for this one. Mhm there. Yeah, it's gonna be two pi times the integral from zero to to your explain X I was this close off. One plus e of crime squared? Yes, on the for dysfunction. What is being able to work effects off ability. The results are tangent. Okay, Is equal to 1/1 plus six square. So this will be all these escapes. Legs would be ableto to buy something to go from zero up to two off arc tangent. Sex comes the square root of one plus one over plus x squared. And then that squared the X. I'm, uh, this surface of revolution about being y axis s banks. Uh, that one is gonna be for two by central, from zero up to eggs. Come to this world of all the same one plus 1/1 plus six squared. That's weird. Yes. Um, so if you pull out the calculator My, this number. December's you about nine point 79 56 This one is about 3. 13 point 772 all night. So those are our our our to don't? Yes. Off revolution area soft bread for Okay, we're talking about the x axis. We're thinking about the wax.