WEBVTT
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we want to find the area of the region and
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closed by these two functions. The 1st 1 is
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in blue. That's Y equals Coast X, and
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the second function is in green. Why equals X
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plus to sign next to the fore? So we
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find by using a graphing calculator that there is actually
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two enclosed regions the 1st 1 here and the 2nd
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1 over here. So we want to find the
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total area. So we're going to be adding these
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two regions area equals area one plus area two.
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So we're going to determine each of these areas separately
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. Area one is equal to what we're going to
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do. An integral. So I didn't say which
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is area when we're going to consider the the left
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most region to be area one. So we're going
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to be integrating from X equals negative. 1.912 two
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X equals negative 1.224 It's going to be our top
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function, minus our bottom function. The top function
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is the green one in this region. So this
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is X. You okay? Here we go.
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X plus two sign for X minus The bottom function
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, which is in Blue Coast X DX. So
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that's area one area to will be computed similarly so
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for area to which is this region the right region
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? Um, we're going to be into getting from
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our left most point which is now negative 1.224 to
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our right most point, which is 0.608 and we're
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going to do our top function minus their bottom function
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. This time I'm the functions play the opposite rules
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. The top function is the blue one now,
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which is co sex and we subtract the bottom function
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which is green so minus X minus to sign for
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X d x. We're allowed to use a into
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an integral calculator for this question. So after we
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compete these two areas and we add them together,
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we get her area. We are rounding to five
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decimal places, which means that our area that we
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obtain is 1.70 for 13 as the total area enclosed
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by both of these regions