http://i9.photobucket.com/albums/a84/MzEva/Picture6-1.png
2007-04-15 03:43:35 · 3 answers · asked by bebe_love_xo 1 in Science & Mathematics ➔ Mathematics
You don't need calculus for this problem if you can visualize the question as the area under two 45-45-90 triangles. You can rearrange these two triangles to make a square, and the area of the square is 81.
However, if you have to use calculus: your equation is the same as ∫ x dx = 81/2 for x = 0 to k. That resolves to k²/2 - 0²/2 = 81/2, or k² = 81 and k = 9.
2007-04-15 03:55:20 · answer #1 · answered by Anonymous · 2⤊ 0⤋
First note that |x| is symmetric around the y-axis
because |-x| = |x|.
So your integral can be simplified to
2 *â«(0..k) x dx,
because |x| = x if x is positive.
Evaluating the integral, gives 2k²/2 = 81
k² = 81
so k = 9.
2007-04-15 06:18:16 · answer #2 · answered by steiner1745 7 · 0⤊ 0⤋
integrate_(-k to k) |x| dx = 2*integrate_(0 to k) x dx
= 2*k^2/2
= k^2
k^2 = 81 ==> k = 9
2007-04-15 04:19:34 · answer #3 · answered by roman_king1 4 · 0⤊ 0⤋