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MHT CET202014 Oct 2020Evening ShiftMathematicsArea Under CurvesActual

The area bounded by the circle x²+y²=16 and lines x=0 and x=2 is

Options

  1. A[4 3 + 8 3 ] sq. units
  2. B1 2 [4 3 + 8 3 ] sq. units
  3. C[4 3 - 8 3 ] sq. units
  4. D1 2 [4 3 - 8 3 ] sq. units

Correct answer

A. [4 3 + 8 3 ] sq. units

Step-by-step solution

Given equation of circle is x²+y²=16 y²=16-x² y= 16-x² Required area is shaded. A=2 ~A ( OABCO ) aligned Area &=2 ₀² 16-x² dx &=2 [ x 2 16-x² + 16 2 ⁻¹ x 4 ]₀² &=2 2 2 12 +8 ⁻¹ 1 2 -0 =2 [2 3 +8 ( 6 ) ]=4 3 + 8 3 aligned

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