NDA2017MathematicsArea Under CurvesActual
The area bounded by the curve |x|+|y|=1 is
Options
- A1 square unit
- B2 2 square units
- C2 square unit
- D2 3 square units
Correct answer
C. 2 square unit
Step-by-step solution
|x|+|y|=1 We know, |x|= array c x, x 0 -x, x 0 array . |x|+|y|=1 is array cc x+y=1 & for x 0, y 0 -x+y=1 & for x 0, y 0 x-y=1 & for x 0, y 0 -x-y=1 & for x 0, y 0 array . If we plot graphs of these equations, we get The curve is symmetrical about x any y -axis. Area =4 Area of AOD aligned & =4 ₀^1 y d x=4 ₀^1(1-x) d x=4 [x- x^2 2 ]₀^1 & =4 [1- 1^2 2 - (0- 0^2 2 ) ] & =4 (1- 1 2 )=4 1 2 =2 aligned