-2integral1/x^2=+2/x. why not -2/x?

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-2integral1/x^2=+2/x. why not -2/x?

2007-07-17 05:14:10 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics

3 answers

I = (- 2) ∫ x^(-2) dx
I = (- 2) x^(-1) / (-1) + C
I = (2) (x^(-1)) + C
I = 2 / x + C

2007-07-17 07:55:33 · answer #1 · answered by Como 7 · 1⤊ 0⤋

if -2/x was a solution the d/dx(-2/x) would equal -2/x^2.

d/dx(-2/x) = -2*d/dx(1/x) = -2*-1/x^2 = 2/x^2 which does not equal -2/x^2. So 2/x is the correct solution.

2007-07-17 13:05:35 · answer #2 · answered by Anonymous · 0⤊ 0⤋

Integral x^2dx = -x^-1

therefore -2 * Integral x^-2 dx = (-2) * (-x^-1) = 2x^-1

2007-07-17 12:22:06 · answer #3 · answered by GTB 7 · 0⤊ 0⤋