NIMCET 2016 Question Paper with solutions

Question : 67 of 120

Marks: +1, -0

The area of the region bounded by the lines y = |x – y| and y = 3 – |x| is;

Solution:

y={|x-1|}=\{\table x-1:x ≥ 1;1-x:x < 1

.....(i)
and

y=3-{|x|}=\{\table3-x:x ≥ 0;3-x:x < 0

....(ii)

Clearly, the two curves meet at (-1,2) and (2,1) Required area

=∫_{-1}^{0}(y_{2}-y_{1})dx+∫_{0}^{1}(y^{2}-y_{1})dx+∫_{1}^{2}(y_{2}-y_{1})dx

=∫_{-1}^{∞}[3+x-(1-x)]dx+∫_{0}^{1}[(3-x)-(1-x)]dx+∫_{1}^{2}[(3-x)(x-1)dx

=4

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