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  • Using the method of integration find the area bounded by the curve |x|+|y|=1.

Q : 11         Using the method of integration find the area bounded by the curve  \small |x|+|y|=1.

                   [Hint: The required region is bounded by lines   \small x+y=1,x-y=1,-x+y=1  and   \small -x-y=1]

                        

Answers (1)

best_answer

We need to find the area of the shaded region ABCD

ar(ABCD)=4ar(AOB)

Coordinates of points A and B are (0,1) and (1,0)

Equation of line through A and B is y=1-x

\\ar(AOB)=\int_{0}^{1}(1-x)dx\\ =[x-\frac{x^{2}}{2}]_{0}^{1}\\ =(1-\frac{1}{2})-0 \\=\frac{1}{2}\ units\\ ar(ABCD)=4ar(AOB)\\ =4\times \frac{1}{2}\\ =2\ units

The area bounded by the curve  \small |x|+|y|=1 is 2 units.

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Sayak

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