₀^a a-x x d x= k 2 , then k=

Step-by-step solution

We have ₀^3 a-x x d x= k 2 Put x=a ^2 d x=a(2 ) d =2 a d When x =0, =0 and when x = a , = 2 aligned & ₀^ 2 a - a ^2 a ^2 (2 a ) d = k 2 & ₀^ 2 ^2 ^2 2( a ) d = k 2 ₀^ 2 2( a ) d = k 2 & ₀^ 2 2 a ^2 ~d = k 2 2 a ₀^ 2 1+ 2 2 ~d = k 2 & ₀^ 2 2 a ^2 ~d = k 2 2 a ₀^ 2 1+ 2 2 ~d = k 2 & a [ ( 2 +0 )-(0+0) ]= k 2 a 2 = k 2 k = a aligned