If the area of the larger portion bounded between the curves x^2+y^2=25 and y=|x-1| is 1 4 (b +c), b, c N , then b+c is equal to

Step-by-step solution

aligned & x ^2+ y ^2=5 & x ^2+( x -1)^2=25 x =4 & x ^2+(- x +1)^2=5 x =-3 & ~A =25 - _ -3 ^4 25- x ^2 dx + 1 2 4 4+ 1 2 3 3 & ~A =25 + 25 2 - [ x 2 25- x ^2 + 25 2 ⁻¹ x 5 ]_ -3 ^4 & ~A =25 + 25 2 - [6+ 25 2 ⁻¹ 4 5 +6+ 25 2 ⁻¹ 3 5 ] & A =25 + 1 2 - 25 2 2 & ~A = 75 4 + 1 2 & ~A = 1 4 (75 +2) & b =75, c =2 & ~b + c =75+2=77 aligned