If a Z ⁺,[x] is greatest integer not more than x and ₀^a 2^ [x] d x=127 , then a=

Step-by-step solution

aligned & ₀^a 2^ [x] d x & = ₀^1 2^0 d x+ ₁^2 2^1 d x+ ₂^3 2^2 d x+ _ a-1 ^a 2^ a-1 d x=127 & 2^0+2^1+2^2+ +2^ a-1 =127 & 1 [2^a-1 ] 2-1 =127 2^a=128 2^a=2^8 a=8 aligned