WEBVTT
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All right. Now sketch the region enclosed by those
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two curves. So this is our XY plane.
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And the first function is why he goes to X
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Cube. So you should look like this. This
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is our by equals two x Q And why he
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goes to X. Okay, it's a street line
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. This is why it goes x in this those
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two eco region since everything is symmetric, uh,
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with respect or region. So those two are exactly
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the same. Um, they have the same area
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, and now we need to find this shaded region
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area. Um, so they will be, um
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yeah, we only need to calculate one side.
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So wait time and then times two. So it
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will be two times. Um, this shaded region
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. Yeah. Um, and, uh, I
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want to calculate this region by taking integral with respect
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to X. Since everything is represented bags All right
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. Right. The next step, we need to
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find the boundary. Correct. Clearly, X goes
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from zero to this point this point x two all
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right and x two should satisfy the those two functions
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, which is X square equals two x, so
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x two should satisfy this equation. Yeah. Since
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extra is not zero, we can cancel one X
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Then we got X squared equals one, which gives
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us X two eco swat. Since X two is
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part, so are integral. That goes from zero
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to one. Okay, um, so then the
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thing inside the integral is the upper curve, minus
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the lower curve. So our upper curve here is
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a straight line X minus glower, curve xq.
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Yeah. Then let's find anti duality of that.
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That will be up half black Square, minus fourth
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. Thanks for you had a boundary one and zero
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. So Well, X equals one we plug in
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. This will give us one half minus or quarter
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, which is a quarter times two is about half
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right minus, we know, actually called zero.
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This term, zero times two is also zero.
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So it's like one half minus zero. Our answer
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will be just 7.5