Question

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

• A. 6
• B. 8
• C. 12
• D. 21

Answer 1

The correct option is C 12

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

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

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

$=2[x-\frac{x^5}{5}{]}_0^1+2[\frac{x^5}{5}-x{]}_1^2$

$=2[1-\frac{1}{5}]+2[\frac{32}{5}-2-\frac{1}{5}+1]$

$=2-\frac{2}{5}+\frac{64}{5}-2-\frac{2}{5}$

$=\frac{60}{5}=12$