`int_(-5)^(5)|x+2|dx`

Explanation

माना `I=int_(-5)^(5)|x+2|dx`
`therefore" "I=int_(-5)^(5)|x+2|dx`
`therefore" "I=int_(-5)^(-2)-(x+2)dx+int_(-2)^(5)(x+2)dx`
`[because int_(a)^(b)f(x)dx=int_(a)^(c)f(x)dx+int_(c)^(b)f(x)dx]`
`rArr" "I=-[(x^(2))/(2)+2x]_(-5)^(-2)+[(x^(2))/(2)+2x]_(-2)^(5)`
`=-[((-2)^(2))/(2)+2(-2)-((-5)^(2))/(2)-2(-5)]+[((5)^(2))/(2)+2(5)-((-2)^(2))/(2)-2(-2)]` ltbr `=-[2-4-(25)/(2)+10]+[(25)/(2)+10-2+4]`
`= 29`