Question

The value of integral $\int |2x^2-18|dx$ will be

• A. $\frac{2}{3}{x}^3-18x+C$ for $x\in (3,5)$
• B. $18x-\frac{2}{3}{x}^3+C$ for $x\in (3,5)$
• C. $\frac{2}{3}{x}^3-18x+C$ for $x\in (2,3)$
• D. $18x-\frac{2}{3}{x}^3+C$ for $x\in (-3,3)$

Answer 1

Answer: (A), (D)

The correct options are
A $\frac{2}{3}{x}^3-18x+C$ for $x\in (3,5)$
D $18x-\frac{2}{3}{x}^3+C$ for $x\in (-3,3)$

To find: $\int |2x^2-18|dx$

Now, roots of $2x^2-18$ are +3 and -3

The function is +ve in the interval $x\in (-\infty ,-3)\cup (3,\infty )$

The function is -ve in $x\in (-3,3)$

$\int |2x^2-18|dx$

$=\int -(2x^2-18)dxforx\in (-3,3)$

$=18x-\frac{2x^3}{3}+C$

$=\int (2x^2-18)forx\in (-3,\infty )\cup (3,\infty )$

$=\frac{2x^3}{3}-18x+C$