Lef  f : R→0,1 be a continuous function. Then which of the following functions (S) has (have) the value zero at some point in the interval?

A)   fx   is positive  and ∫0π2ftsint dt  is positive Hence, fx+∫0π2ftsint dt is positiveB) fx=x9−fxf0=0−f0= negativef1=1−f1=positive∴fx=0for atleast one x∈0,1C)fx=x−∫0π2−xftcos t dt f0=0−∫0π2ftcost dt  is negativef1=1−f0π2−1ftcost dt is positive∴fx=0 for atleast one x∈0,1D)f0=e0−∫00ft sint dt =1f1=e−∫01ft sint dt =Positve valuef1x=ex−fx sinx >0 for x∈0,1