If integrating |2x|dx from -k to k equals 18 and k>0, then what is the value of k?

Question

many thanks!

Answer 1

integral | 2 x | dx =

2 integral | x | dx =

2 ( x ^ 2 ) * sgn ( x ) + C =

integral | 2 x | dx from - k to k =

k ^ 2 - [ ( k ^ 2 ) * ( - 1 ) ] =

k ^ 2 + k ^ 2 =

2 k ^ 2

2 k ^ 2 = 18 Divide both sides by 2

k ^ 2 = 9

k = sqrt ( 9 ) = ± 3

integral | 2 x | dx from - 3 to 3 = 18

k = 3

Answer 2

2 integral | x | dx =

2 ( x ^ 2 ) / 2 * sgn ( x ) + C =

( x ^ 2 ) * sgn ( x ) + C =