If f(x)= array cl 6 x^2+1 4 x^3+2 x+3 , & , 0 x 1 x^2+1 & , 1 x 2 array . then ₀^2 f(x) d x=

Step-by-step solution

aligned & f(x)= array cc 6 x^2+1 4 x^3+2 x+3 , & 0 x 1 x^2+1, & 1 x 2 ₀^2 f(x) d x= ₀^1 f(x) d x+ ₁^2 f(x) d x array . & = ₀^1 6 x^2+1 4 x^3+2 x+3 d x+ ₁^2 (x^2+1 ) d x aligned aligned & = 1 2 ₀^1 12 x^2+2 4 x^3+2 x+3 d x+ ₁^2 (x^2+1 ) d x & = [ 1 2 (4 x^3+2 x+3 ) ]₀^1+ [ x^3 3 +x ]₁^2 & = 1 2 9- 1 2 3+ 8 3 +2- 1 3 -1= 1 2 3+ 10 3 aligned