Determine the area under the curve `y=sqrt(a^(2)-x^(2))` included between the lines x =0 and x = a.

Answer

N/a

Explanation

Given equation of the curve is `y=sqrt(a^(2)-x^(2))`.
`rArry^(2)=a^(2)-x^(2)rArry^(22)+x^(2)=a^(2)`

`:. " Required area of shaded region," A=int_(0)^(a)sqrt(a^(2)+x^(2))+(a^(2))/2sin^(-1)(x)/a]_(0)^(a)`
`=[0+(a^(2))/2sin^(-1)(1)-0-a^(2)/2sin^(-1)0]`
`=a^(2)/2 . pi/2=(pia^(2))/4" sq units"`