Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET201825 Apr 2018Morning ShiftMathematicsArea Under CurvesActual

The area (in sq. units) of the region lying in the first quadrant and enclosed by the X -axis, the straight line x - 3 y = 0 and the circle x 2 + y 2 = 4 is

Options

  1. Aπ 3
  2. B2 π 3
  3. Cπ 2 3
  4. D2 π 3 2

Correct answer

A. π 3

Step-by-step solution

Required area = A r ∆ O A B + ∫ 3 2 4 - x 2 d x Now, A r ∆ O A B = 1 2 × 3 × 1 = 3 2     . . . i And, let I = ∫ 3 2 4 - x 2 d x = 1 2 x 4 - x 2 + 4 2 sin - 1 x 2 3 2 = 1 2 · 2 · 4 - 4 + 2 sin - 1 2 2 - 3 2 + 2 sin - 1 3 2 = 2 × π 2 - 3 2 + 2 π 3 = π 3 - 3 2     . . . i i By i   &   i i , we get Required area = π 3   sq . units .

Practice Area Under Curves on Quantrex Academy →

More from Area Under Curves

Find the area bounded by the curve y = |2 - x| , the x –axis, and the lines x = 0 and x = 5 2026The area enclosed by the curve y = -x^2 and the line x + y + 2 = 0 is 2026The area of the region bounded by the line y = x + 2 and the curve x = -y^2 is 2026The area of the region in the first quadrant enclosed by the x -axis, the line x = 3 ,y and the circle x^2 + y^2 = 4 is 2026The area of the region bounded by the curve y^2 = x^3 , the y -axis and the lines y = 1 and y = 8 is 2026The area enclosed by the curve x = 3 , y = 3 is 2026The area in square units of the region bounded by the curve y = 16 - x^2 and lines x = 0, x = 4 above the X-axis is 2026The area bounded by the curves y = |x| - 1 and y = -|x| + 1 is 2026 Full Area Under Curves list All AP EAMCET PYQs