Question

The value of $\int\limits_{0}^{5} \max \left\{x^{2}, 6 x-8\right\} d x$ is

• A. 72
• B. 125
• C. 43
• D. 69

Answer 1

Answer: (C)

$\int\limits_{0}^{5} \max \left\{x^{2}, 6 x-8\right) d x$
Let $f(x)=x^{2}-6 x+8$
$=(x-4)(x-2)$
$\therefore $ For $x \in[0,2] \cup[4,5], f(x)>0$
and in $x \in[2,4], f(x)<0$
$\int\limits_{0}^{5} \max \left(x^{2}, 6 x-8\right)=\int\limits_{0}^{2} x^{2} d x+\int\limits_{2}^{4}(6 x-8) d x+\int\limits_{4}^{5} x^{2} d x$
$=\frac{8}{3}+20+\frac{61}{3}=43$