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COMEDK2024Evening ShiftMathematicsArea Under CurvesActual

The area bounded by the curve y= x, x=0 and x= is

Options

  1. A2 sq units
  2. B1 sq units
  3. C4 sq units
  4. D3 sq units

Correct answer

A. 2 sq units

Step-by-step solution

The area A bounded by the curve y = x between x = 0 and x = is given by the integral of the absolute value of the function, because the curve crosses the x-axis at x = /2 . A = ₀^ | x| dx Splitting the integral at the point where x = 0 , which is x = /2 : A = ₀^ /2 x dx + _ /2 ^ - x dx Evaluating the integrals: A = [ x]₀^ /2 - [ x]_ /2 ^ A = ( ( /2) - (0)) - ( ( ) - ( /2)) A = (1 - 0) - (0 - 1) A = 1 + 1 = 2 sq units. Answer: 2 sq units

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