Paragraph: Let I = ₀^ 2 f(x) g(x) d x , where f(x)= x and g(x)= x+ x+1 . Question: What is I equal to?

Step-by-step solution

Given that f(x)= x and g(x) x+ x+1 Let I= ₀^ 2 f(x) g(x) d x= ₀^ 2 x x+ x+1 d x .....(i) aligned & I= ₀^ 2 ( 2 -x ) ( 2 -x )+ ( 2 -x )+1 d x & I= ₀^ 2 x x+ x+1 d x ....(ii) aligned Adding equation (i) and (ii), we get 2 I= ₀^ 2 x+ x x+ x+1 d x aligned & = ₀^ 2 (1- 1 x+ x+1 ) d x & = ₀^ 2 1 d n- ₀^ 2 1 x+ x+1 d x aligned from solution of previous question aligned & 2 I = ₀^ 2 1 dx - 2= 2 - 2 & I = 4 - 2 2 aligned