# What is the integral of 9x

## Applying Mathematics HUM 4, textbook

119 If the domain of f is an interval or all of R and if F is an antiderivative of f, then all other antiderivatives are obtained by adding any constant function to F. GeoGebra Integral [, ] TI Nspire integral (Expr, Var) (Note: The integration constant is not displayed.) 408 Check whether the function F with F (x) = 5x 2 - 3x + 2 or the function G with G (x) = 5x 2 + 3x - 2 is an antiderivative of the function f with f (x) = 10x + 3. The derivative of F is F 'with F' (x) = 10x - 3 ≠ f (x), so F is not an antiderivative of f. The derivative of G is G 'with G' (x) = 10x + 3 = f (x), so G is an antiderivative of f. 409 Check whether the function F with F (x) = 5x 3 + 4x 2 - 3x + 7 or the function G with G (x) = 5x 3 - 4x 2 - 7x is an antiderivative of the function f with f (x) = 15x 2 + 8x - 3. 410 Show that both F with F (x) = 3x 2 + 4x + 7 and G with G (x) = 3x 2 + 4x - 9 are antiderivatives of the function f with f (x) = 6x + 4. 411 Tick which of the functions are parent functions of f 'with f' (x) = 12x 3 - 9x 2 + 8x - 1. A f with f (x) = 36x 2 - 18 x + 8 B f with f (x) = 3x 4 - 3 x 3 + 4x 2 - x C f with f (x) = 4x 4 - 4.5x 3 + 8x 2 - x D f with f (x) = 3x 4 - 3 x 3 + 4x 2 - x + 17 E f with f (x) = 4x 4 - 4.5x 3 + 8x 2 - x - 124 412 Arrange the Functions f assign the correct antiderivative F to. a. f (x) = 12x 3 - 6x 2 + 4x - 1 AF (x) = 4x 4 - 3x 3 + 4x 2 - x + 5 BF (x) = 1.5 x 4 + 3x 3 - 2.5x 2 + 8x + 1 b. f (x) = 6x 3 + 9x 2 - 5x + 8 CF (x) = 3x 4 - 2x 3 + 2x 2 - x - 1 DF (x) = 2x 4 + 4.5x 3 - 5x 2 + 8x + 3 413 Find three possible antiderivatives of fa f (x) = 6x 2 + 3 b. f (x) = - 8x + 7 c. f (x) = 16x 3 - 12x d. f (x) = 8x 3 + 9x 2 - 2x + 7 414 Find three different functions whose derivative is the given polynomial function f. a. f (x) = 4x 3 - 6x 2 - 2x + 3 b. f (x) = 10x 4 - 9x 2 + x c. f (x) = 1 d. f (x) = 0 415 Show the graph of three different antiderivatives of the linear function f with f (x) = x + 1 in a diagram. 416 Show the graph of three different antiderivatives of the quadratic function f with f (x) = 3x 2 in a diagram. If F is an antiderivative of f, then also F + c calculate antiderivative ggb / tns n38s2b recognize an antiderivative CB, D: B, D: B: B: B,, B, BB, 4.1 Das indefinite integral For testing purposes only - property of the publisher öbv

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