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AP EAMCET202125 Aug 2021Morning ShiftMathematicsArea Under CurvesActual

If the area of the region enclosed by the curve x^2+y^2=16 and then lines x=2 and x=3 is (3 7 -4 3 - 8 3 +k ) sq units, then k equals

Options

  1. A16 ⁻¹ ( 3 4 )
  2. B8 ⁻¹ ( 3 4 )
  3. C4 ⁻¹ ( 3 4 )
  4. D2 ⁻¹ ( 3 4 )

Correct answer

A. 16 ⁻¹ ( 3 4 )

Step-by-step solution

Area of region enclosed by the curve x^2+y^2=16 and line x=2 and x=3 is aligned & A= ₂^3 16-x^2 d x & A= [ x 2 16-x^2 +8 ⁻¹ x 4 ]₂^3 & 3 7 -4 3 - 8 3 +k & = ( 3 2 7 +8 ⁻¹ 3 4 )- (2 3 +8 ⁻¹ 2 4 ) & 3 7 -4 3 - 8 3 +k & = 3 2 7 +8 ⁻¹ 3 4 -2 3 - 8 6 & = 1 2 (3 7 +16 ⁻¹ 3 4 -4 3 - 8 3 ) & k=16 ⁻¹ ( 3 4 ) & aligned

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