Question

The value of the integral $∫^2_{-2}\frac{ |x^3+x|}{(e^x|x|+1)}dx$ is equal to:

• A. $5e^2$
• B. $3e^{–2}$
• C. 4
• D. 6

Answer 1

Answer: (D)

6

Answer 2

$I = ∫^2_{-2}\frac{ |x^3+x|}{(e^x|x|+1)}dx.....(i)$

$I = ∫^2_{-2}\frac{ |x^3+x|}{(e^x|x|+1)}dx.....(ii)$

$2I = ∫^2_{-2} |x^3+x|dx$

$2I = 2 ∫^2_0(x^3+x)dx$

$I = ∫^2_0 (x^3+x)dx$

= $\bigg(\frac{16}{4}+\frac{4}{2}\bigg)-0$

= $4+2 = 6$

Hence, the correct option is (D): $6$