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COMEDK2025MathematicsArea Under CurvesActual

Area of the region bounded by the curve y= x between x=- 2 and x= is-----

Options

  1. A2 sq units
  2. B3 sq units
  3. C1 sq units
  4. D4 sq units

Correct answer

B. 3 sq units

Step-by-step solution

The area A bounded by the curve y = x between x = - 2 and x = is given by the integral A = _ - /2 ^ | x| dx . The function x is positive in the interval [- /2, /2] and negative in the interval [ /2, ] . Therefore, the integral is split as A = _ - /2 ^ /2 x dx + _ /2 ^ - x dx . Evaluating the first integral: _ - /2 ^ /2 x dx = [ x]_ - /2 ^ /2 = ( /2) - (- /2) = 1 - (-1) = 2 . Evaluating the second integral: - _ /2 ^ x dx = -[ x]_ /2 ^ = -( - ( /2)) = -(0 - 1) = 1 . The total area is A = 2 + 1 = 3 sq units. Answer: 3

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