1) If f(x) = x2, g(x) = 2x, $0\leq x \leq2$ then the value of $I(x)= \int_{0}^{2} max(f(x),g(x) ) $ is A) $\frac{10}{3}$ B) $\frac{1}{3}$ C) $\frac{11}{3}$ D) 32 Answer: Option DExplanation:Let r(x) = f(x).g(x) = x2..2x= 2 x3 r'(x) =6x2 Put 6 x2 =0, $\therefore$ x=0 Max r(x) =2 (2)3 =16 or Max (f(x) ,g(x) )=16 $I(x)=\int_{0}^{2} 16 dx$ $I(x)=[ 16x ]_0^2=32-0=32$
