₀^ 2 300 x+100 x x+ x ~d x=

Step-by-step solution

Evaluate the integral: I = ₀^ 2 300 x+100 x x+ x , d x Apply the transformation x 2 - x , using the identity _a^b f(x) , d x = _a^b f(a+b-x) , d x : I = ₀^ 2 300 x+100 x x+ x , d x Add this to the original integral: 2I = ₀^ 2 400 x+400 x x+ x , d x = 400 ₀^ 2 , d x Evaluate the integral: 2I = 400 2 = 200 Result: I = 100 This corresponds to option A .