Question

The value of $\int |x^2+2|dx$ is

• A. $-\frac{x^3}{3}-3x+C$
• B. $\frac{x^3}{3}+3x+C$
• C. $\frac{x^3}{3}+2x+C$
• D. $(\frac{x^3}{3}+2x)\text{sgn}x+C$

Answer 1

The correct option is C $\frac{x^3}{3}+2x+C$

Let $I=\int |x^2+2|dx$
We know
$x^2+2>0\forall x\in R$

$\Rightarrow I=\int (x^2+2)dx$

$\Rightarrow I=\frac{x^3}{3}+2x+C$