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BITSAT2018MathematicsArea Under CurvesActual

The area of the region included between the curves x 2 + y 2 = a 2 and x + y = a a > 0 is

Options

  1. Aπ - 2 3 a 2 sq units
  2. B2 3 - π a 2 sq units
  3. C2 3 π a 2 sq units
  4. Dπ + 2 3 a 2 sq units

Correct answer

A. π - 2 3 a 2 sq units

Step-by-step solution

Given curves are x + y = a       . . . i and x 2 + y 2 = a 2       . . . ii Now, required areas = 4 [shaded area in the first quadrant] = 4 π a 2 4 - ∫ 0 a a - x 2 d x [from Eqs. (i) and (ii)] = 4 π a 2 4 - ∫ 0 a a + x - 2 a x d x = 4 π a 2 4 - 4 a x + x 2 2 - 4 3 a x 3 / 2 0 a = π - 2 3 a 2 sq units Hence, option (a) is correct.

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