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Understanding Antidifferentiation: Graphical Interpretation & Properties

Antidifferentiation is the reverse of differentiation, integral to calculus. Learn about its properties, including integration of 1/x and (ax + b)-1 functions. Explore the relationship between the graph of an antiderivative function and the original function's graph. The graphical interpretation highlights the gradient function and the general shape of the antiderivative graph.

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Understanding Antidifferentiation: Graphical Interpretation & Properties

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  1. 9A Antidifferentiation – the reverse of differentiation

  2. 9A Antidifferentiation

  3. 9A Antidifferentiationproperties

  4. 9A Antidifferentiation

  5. 9A Antidifferentiation

  6. 9A Antidifferentiationintegration of where

  7. 9A Antidifferentiationintegration of where

  8. 9A Antidifferentiationintegration of 1/x

  9. 9A Antidiffferentiation integration of 1/x

  10. 9A Antidifferentiationintegration of (ax + b)-1

  11. 9A Antidifferentiationintegration of (ax + b)-1

  12. 9A Antidifferentiation

  13. 9A Antidifferentiation

  14. 9A Antidifferentiation

  15. 9A Antidifferentiation The relationship between the graph of an antiderivative function and the graph of the original function. is the gradient function of the antiderivative function , general shape of the graph of the antiderivative is determined by increasing the degree of the polynomial by one, the x-intercepts of become the turning points on the graph of when is above the x-axis, the gradient of is positive, when is below the x-axis, the gradient of is negative.

  16. 9A Antidifferentiation The relationship between the graph of an antiderivative function and the graph of the original function. Sketch the graph of the antiderivative function from the graph of the gradient function as shown.

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