Discussion Forum

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 

Answer:

Explanation:

Let r(x) = f(x).g(x)

 = x^2..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

 $I(x)=\int_{0}^{2} 16 dx$

$I(x)=[ 16x ]_0^2=32-0=32$