Problem 18 Easy Difficulty

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

$ y = \sqrt{x - 1} $ , $ x - y = 1 $

Answer

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Video Transcript

again. Let's draw those two curves first. So say this is our acts My plane in the first Carvey's actually, uh, he's just a squared X move A shifted to the right by one. So we know, um, a square hotel fax It's look like this. So he's shifted by once we start from one, and it goes like this. The second is the street line X minus Y equals one. So but why go to zero X equals one? So across this point and x zero by cosa naked across this part our street flying is here. This is our street line. Next, minus y. You close one. Okay. Ah, and then close area is the shaded regions Now, Alice, trading for in the area. Um, you know, to find this outer area, we need to take the integral by the respect, respect to X or respect why it depends on ah how you represent those functions. Say, since I Personally, I don't like this square root because if you remember the square root of something, the anti duty off that is it's very difficult to remember and looks ugly. So here I'll reform the first function. So I take square on both side I'LL get up Thanks. He closed Tio one plus y square. Hey, And remember over, um our wise quater than zero. The greater the co two zero right, Because the white goes to a square root off something So it always known Active on this since the first function I represented by Why this I also want to represent But why? So I do Here is some I mean why to the other side. So the second function will be activity close to one plus one. Right? Um after this so many in a row with respect. Why? And let's find hungry No, a star from zero. And what about this point? The basis our way too. That was so bad off. Why To just say this happens when y plus by square yukos one plus y And we know why too cannot be zero. Which means I lied too. Ecos water because this equation will give us to swoosh is one of them yourself. One and another is zero since white who is not zero. So it has to be one on our boundary with coast from zero to one in the things I the integral. Always red curve minus the left curve or red car abuse of a bus boy. And now our left curve. Here is this one plus life work. Okay, now, Andy. Dear God, this is one half those one canceled. So the anti dirty off. Why is what? Half white square? Minus one cube. My third one like you. Hey, you graduated and in one zero. So Plugin Lycos one. This is what Half minus one third of the cheese. One six in the second term zero. So fix Ivancic will be our answer.