For a function f(x) (x≥1) satisfying f(x)=(logex)2−∫1etf(t)dt, answer the questions as below.(a) Find f(x) and the y-coordinate of the inflection point of the curve y=f(x).(b) Find the area of the figure bounded by the tangent line of y=f(x) at the point (e, f(e)), the curve y=f(x) and the line x=1. calculusintegrationfunctionlogarithmsanalytic geometrygeometryderivative