Question

If $I={\int }_{-2}^2|1-x^4|dx,$ then $I$ equals

• A. $6$
• B. $8$
• C. $12$
• D. $21$

Answer 1

Answer: (C)

$12$

As, $|1-x^4|$ is an even function, so

$I=2{\int }_0^2|1-x^4|dx$

$=2{\int }_0^1(1-x^4)dx+2{\int }_1^2(x^4-1)dx$

$=2{(x-\frac{x^5}{5})}_0^1+2{(\frac{x^5}{5}-x)}_1^2$

$=2(1-\frac{1}{5})+2(\frac{32}{5}-2-\frac{1}{5}+1)=12$