WEBVTT
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Let's use a trick substitution for this integral because the
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denominator inside the radical is of the form a squared
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, minus X squared. I would go ahead and
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use X equal scientific era, then DX. It's
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because I'm dead so we can rewrite this integral.
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And we do have a definite on girl here,
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So we do have the opportunity or not necessary.
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It's not required, but it can simplify your work
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to rewrite these limits of integration in terms of fatal
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if possible. So here plug in X equals zero
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and then recall when we do it. Troops up
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of this form signed data you require. That data
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is in between negative, however too entirely too.
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So the only solution to this equation and dishonorable up
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here is state a equal zero. So our new
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lower limit will still be zero and then plug in
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the upper limit for X in. The only solution
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in this interval that makes this possible is PIRA for
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so that's our new upper limit. And then we
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see X Square up here in the numerator, so
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that becomes science squared after the substitution and then we
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have DX. So that's co sign D data.
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And then in the denominator, we have one minus
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X squared inside. The radical selections come to the
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side to evaluate this and then use the protector in
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Toronto for sign and co sign to write. This
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is co sign squared, and then you can evaluate
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. This is just cosign data. So that's your
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denominator. And then we could go ahead and cross
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off those one half. So here we're left with
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just pie before and then we have just signed squared
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only. So here I would use tohave angle formula
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for science. Queer. That's one minus co sign
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to date over, too. And then here I'm
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just pulling out the one half and then I have
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one minus course I into data left over. So
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that's one half. Now it's in a very that's
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data minus scientist eight over, too zero pyro for
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. And then let's just go ahead and plug those
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and points in so plugging Piper for first. So
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we have a pilot or for minus sign pi over
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too, over two, and then when we plug
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in zero both terms or zero, we have zero
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minus sign zero over to, so there's nothing to
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subtract and then sign a pie over to is just
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one. So we just have pav rate. So
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we write this pie over eight and then minus one
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over four, and this is after we did distribute
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the one half, and that's your final answer.