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
If integrating |2x|dx from -k to k equals 18 and k>0, then what is the value of k?
many thanks!
2 answers
2 integral | x | dx =
2 ( x ^ 2 ) / 2 * sgn ( x ) + C =
( x ^ 2 ) * sgn ( x ) + C =
2 ( x ^ 2 ) / 2 * sgn ( x ) + C =
( x ^ 2 ) * sgn ( x ) + C =