anonymous
  • anonymous
find the area bounded by the curve {(x,y): |x-1| <= y <= sqrt (5- x^2)}
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
are these the parameters \[\left| x-1\right|\le y \le \sqrt{5}-x^{2}\]?
anonymous
  • anonymous
yes
goformit100
  • goformit100
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anonymous
  • anonymous
any ans pls???
anonymous
  • anonymous
Maybe it would help to draw the area you have to find (ignore the bottom half of the circle): |dw:1378050488377:dw|
anonymous
  • anonymous
Split up the area along this vertical line: |dw:1378050705596:dw| Then the line to the left is \(y=-x+1\) and the line to the right is \(y=x-1\).
anonymous
  • anonymous
The area is given by \[A=\int_a^0\left(\sqrt{5-x^2}-(-x+1)\right)~dx+\int_0^b \left(\sqrt{5-x^2}-(x-1)\right)~dx\] where \((a,c)\) and \((b,d)\) are the intersection points of the lines with the semicircle: |dw:1378051625875:dw|
anonymous
  • anonymous
Slight correction:\(\color{blue}{\text{Originally Posted by}}\) @SithsAndGiggles The area is given by \[A=\color{red}{\int_a^1}\left(\sqrt{5-x^2}-(-x+1)\right)~dx+\color{red}{\int_1^b} \left(\sqrt{5-x^2}-(x-1)\right)~dx\] \(\color{blue}{\text{End of Quote}}\)

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