MathematicsMedium210×since 2002Q3331Let f(x)f(x)f(x) be a function satisfying f′(x)=f(x)f'(x)=f(x)f′(x)=f(x) with f(0)=1f(0)=1f(0)=1 and g(x)g(x)g(x) be a function that satisfies f(x)+g(x)=x2f\left( x \right) + g\left( x \right) = {x^2}f(x)+g(x)=x2. Then the value of the integral ∫01f(x)g(x)dx,\int\limits_0^1 {f\left( x \right)g\left( x \right)dx,}0∫1f(x)g(x)dx, isAe+e22+52e + {{{e^2}} \over 2} + {5 \over 2}e+2e2+25Be−e22−52e - {{{e^2}} \over 2} - {5 \over 2}e−2e2−25Ce+e22−32e + {{{e^2}} \over 2} - {3 \over 2}e+2e2−23De−e22−32e - {{{e^2}} \over 2} - {3 \over 2}e−2e2−23Check answerSkip