Question

If $f(x) = x^2 , g(x) = 2x,0 \leq x \leq 2$ then the value of $I(x) = \int\limits_0^2 max (f(x), g(x))$ is

• A. $\frac{10}{3}$
• B. $\frac{1}{3}$
• C. $\frac{11}{3}$
• D. 32

Answer 1

Answer: (D)

32

Answer 2

Let $r\left(x\right) = f\left(x\right).g\left(x\right)$ $=x^{2} .2x = 2x^{3}$ $r'\left(x\right) = 6x^{2}$ Put $6x^{2} = 0 , \, \, \therefore x = 0$ Max $r\left(x\right)=2\left(2\right)^{3} = 16$ or Max $\left(f\left(x\right),g\left(x\right)\right) = 16$ $I\left(x\right)= \int^{2}_{0} 16dx$ $I\left(x\right) = \left[16x\right]^{2}_{0} = 32 -0=32$