f(x) = x(2-x)^2?

1 ⤊

Find the most general antiderivative of the function. (Check your answer by diffferentiation.

2007-10-24 06:27:05 · 3 answers · asked by sammiballer99 1 in Science & Mathematics ➔ Mathematics

I = ∫ x(4 - 4x + x²) dx
I = ∫ 4x - 4x² + x³ dx
I = 2x² - 4x³/3 + x^4 / 4 + C

2007-10-24 11:09:42 · answer #1 · answered by Como 7 · 0⤊ 0⤋

x(2-x)Â² = xÂ³ - 4xÂ² + 4x
Integration yields : x^4/4 - 4xÂ³/3 + 4xÂ²/2 + C

2007-10-24 13:52:53 · answer #2 · answered by ?????? 7 · 0⤊ 0⤋

first multiply it out so you have a polynomial

f(x) = (4-4x+x^2)x
f(x) = 4x-4x^2+x^3

F(x) = 4x^2/2 - 4x^3/3 + x^4/4

2007-10-24 13:31:02 · answer #3 · answered by Kaila G 3 · 1⤊ 0⤋