A) \[0\,\,sq\,\,unit\]
B) \[1\,\,sq\,\,unit\]
C) \[2\,\,sq\,\,unit\]
D) \[4\,\,sq\,\,unit\]
Correct Answer: C
Solution :
Given equation of curve is \[|x|+|y|\,\,=1\] \[\therefore \]Required area of curve \[=\]Area of curve\[ABCD\] \[=4\]area of curve\[OAB\] \[=4\int_{0}^{1}{(1-x)}\,dx\] \[=4\left[ x-\frac{{{x}^{2}}}{2} \right]_{0}^{1}\] \[=4\left[ 1-\frac{1}{2} \right]=2\,\,sq\,\,unit\] Alternative Solution: It is clear from the figure that given curve is a square whose length is\[\sqrt{2}\]. \[\therefore \]Area of square\[={{(\sqrt{2})}^{2}}\] \[=2\,\,sq\,\,unit\]You need to login to perform this action.
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