Question

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

• A. 72
• B. 125
• C. 43
• D. 69

Answer 1

Answer: (C)

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