Problem 15 Easy Difficulty

Sketch the region enclosed by the given curves and find its area.

$ y = \sec^2 x $ , $ y = 8 \cos x $ , $ \frac{-\pi}{3} \le x \le \frac{\pi}{3} $

Answer

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Video Transcript

on this problem. We need to sketch the reason enclosed by those two curves so less draw this excellent playing first. And as we can see, the second way is much easier to draw. And we know our acts are don't change goes from negative pie over three to pilot it. So assuming this is pi over three, this is an active power three And here is positive pirate story Marcos i X, where acts decodes to zero You know, this is a human function. Sorry. Somatic along by axis it's over axe equal to zero this seacoast eight And we know that X equals Tau pi or three co sign pie with raise one. But I have So that's where you coast for Oh, this's symmetric. It's also equals for So why Yukos Who ate costar Max? You look like that's okay. Is this some? Hi. He goes to coz I ate Kovacs the second hand The first term here, um is second ex square and we know the second act Square. It's just well, our co Thanks. Where there's one over holds flying next square. Okay, um so the X is equal to zero This seacoast What? Okay, and the next he goes to pie or three on me This coastline power threes have. So we'LL have square is one quarter and receive call for enquiries for So actually intersection point is exactly off the ends off co sacks of endpoints connective pile of three and a positive Powerfully, there's function shall look like this. Uh, we got this in closed area. Now our next step is to find this area. So ah s we see all the things representative acts. Take them to a girl with respect to X and the monk raving already. Phone. It's just a knack. Your pile of three to pilot and being inside the injured girl. It's on upper curve up liquor vis aged costar X minus the Laura curb searches of Second X Square. Now let's find the continuity of of this on. So the first term will be eight science ex, you know, and figurative Allco sex is just sex, you know, if you remember, Auntie, do it. Eve for second acts is actually tension. Tex, are you can If you don't remember, you can check the chart off the anti do it. It I mean the only value at the Congaree ex Echoes to Pirate three and taxi close to nag. Plan three. All right, two million extra close to pyro three. We know. Sign Power three squared to me. Over to sell these for squirrel. Three minus in tangent. Um, Hanjin Power three square three. Okay, miners, plebian pi X equals to Nike Air Power three. So this was inactive for squirmed three love. It's worth three grand, so our answer will be on six square.