Question

$\int_{}^{}{x|x|}$dx =

• A. $\frac{x^{3}}{3}$
• B. $\frac{x^{2}|x|}{3}$
• C. $\frac{x^{2}|x|}{2}$
• D. None

Answer 1

Answer: (B)

$\frac{x^{2}|x|}{3}$

Answer 2

I =. |x| dx = $\int_{}^{}{|x|}$ . x dx

(Integrating by parts taking |x| as first function)

= |x| . – $\int_{}^{}\frac{|x|}{x}$ . $\frac{x^{2}}{2}$dx = $\frac{x^{2}|x|}{2}$

– $\frac{1}{2}$ x dxŽ I $\left( 1 + \frac{1}{2} \right)$ = $\frac{x^{2}|x|}{2}$ Ž I = $\frac{1}{3}x^{2}|x|$