The value of integral _ -2 ^0 (x^3+3 x^2+3 x+5+(x+1) (x+1) ) d x is equal to

Step-by-step solution

Let aligned I & = _ -2 ^0 [x^3+3 x^2+3 x+5+(x+1) (x+1) ] d x & = _ -2 ^0 [(x+1)^3+4+(x+1) (x+1) ] d x aligned array ll & Put x+1=t d x=d t & I= _ -1 ^1 (t^3+4+t t ) d t array Since t^3 and t t are odd functions. I= _ -1 ^1 4 d t=4[t]_ -1 ^1=8 [Note: The answer of the question is not mentioned as an option.]