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Find the most general f. Use C for the constant of the first anti-derivative and D for the constant
of the second anti-derivative.
f ''(x) = 4x + sin x
Solution
f'(x) = int f"(x) = int 4x+sin(x) dx = 2x2 - cos(x) + C1
f(x) = int f'(x) dx = int 2x2 - cos(x) + C1 dx =
2/3 x3 - sin(x) + C1x + C2
where C1 and C2 are constants.

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Find the most general f. Use C for the constant of the first anti-de.pdf

  • 1. Find the most general f. Use C for the constant of the first anti-derivative and D for the constant of the second anti-derivative. f ''(x) = 4x + sin x Solution f'(x) = int f"(x) = int 4x+sin(x) dx = 2x2 - cos(x) + C1 f(x) = int f'(x) dx = int 2x2 - cos(x) + C1 dx = 2/3 x3 - sin(x) + C1x + C2 where C1 and C2 are constants.