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Integral Calculus

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18 Mar 2010 13:55:55 IST

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Hey Guys..Please help me..Very urgent..Find the area within the curve modulus x+modulus y=1..please

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Hey Guys..Please help me..Very urgent..Find the area within the curve modulus x+modulus y=1..please help me..

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Deepak Aggarwal

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Joined: 9 May 2009

Posts: 766

18 Mar 2010 19:18:49 IST

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This is the graph of |x| + |y| = 1.

So, area within the curve = area of square ABCD = 2 sq. units.

or, by integration,

area within the curve = 4 times area of triangle AOB = 4 int x from 0 to 1 (1 - x).dx = 4(x - (x²/2)) with limit of x from 0 to 1

= 4(1 - (1/2)) = 4(1/2) = 2 sq. units.

How to draw the graph

|x| + |y| = 1

For x,y>0; eq. is x + y = 1

For x>0 and y<0; eq. is x - y =1

For x<0 and y>0; eq. is - x + y =1

For x,y<0; eq. is - x - y = 1

illuminatti

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Joined: 19 Feb 2010

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24 Mar 2010 10:34:40 IST

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