The area (in sq units) of the minor segment bounded by the circle x^2+y^2=a^2 and the line x= a 2 is

Step-by-step solution

By symmetry about the x-axis, A = 2 _ a/ 2 ^ a a^2-x^2 dx Using a^2-x^2 dx = x 2 a^2-x^2 + a^2 2 ⁻¹ ( x a ) At upper limit x = a : 0 + a^2 2 2 = a^2 4 At lower limit x = a 2 : a 2 2 a 2 + a^2 2 4 = a^2 4 + a^2 8 A = 2 [ a^2 4 - a^2 4 - a^2 8 ] = 2 [ a^2 8 - a^2 4 ] = a^2 4 - a^2 2 = a^2 4 ( - 2)