The area (in sq. units) of the smaller part of the circle x^2+y^2= a ^2 cut off by the line x= a 2 is

Step-by-step solution

Substitute x= a 2 in x^2+y^2= a ^2 , we get a ^2 2 +y^2= a ^2 y= a 2 Required area aligned & =2 _ a 2 ^a a^2-x^2 d x & =2 [ x 2 a^2-x^2 + a^2 2 ⁻¹ ( x a ) ]_ a 2 ^2 & =2 [0+ a^2 2 2 ]- [ a 2 2 a^2- a^2 2 + a^2 2 4 ] & =2 [ a^2 4 - a^2 4 - a^2 8 ] & = a^2 2 | -1- 2 | & = a^2 2 | 2 -1 | aligned