JEE Main20249 Apr 2024Morning ShiftMathematicsArea Under CurvesActual
The parabola y^2=4 x divides the area of the circle x^2+y^2=5 in two parts. The area of the smaller part is equal to:
Options
- A1 3 +5 ⁻¹ ( 2 5 )
- B1 3 + 5 ⁻¹ ( 2 5 )
- C2 3 +5 ⁻¹ ( 2 5 )
- D2 3 + 5 ⁻¹ ( 2 5 )
Correct answer
C. 2 3 +5 ⁻¹ ( 2 5 )
Step-by-step solution
aligned & y^2=4 x & x^2+y^2=5 aligned Area of shaded region as shown in the figure will be aligned & A ₁= ₀^1 4 x dx + ₁^ 5 5- x ^2 dx & = 4 3 [ x ^ 3 2 ]₀^1+ [ x 2 5- x ^2 + 5 2 ⁻¹ x 5 ]₁^ 5 & = 1 3 + 5 4 - 5 2 ⁻¹ ( 1 5 ) & Required Area =2 ~A ₁ & = 2 3 + 5 2 -5 ⁻¹ ( 1 5 ) & = 2 3 +5 ( 2 - ⁻¹ 1 5 ) & = 2 3 +5 ⁻¹ 1 5 & = 2 3 +5 ⁻¹ ( 2 5 ) aligned