Key Concepts and the Fundamental Theorem (Year 11-12)
Free printable Year 11-12 Mathematical Methods worksheet: the meaning of antidifferentiation, the constant of integration, and the Fundamental Theorem of Calculus.
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Year 11-12 · Math worksheet
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Date
Math
Integration: Key Concepts and the Fundamental Theorem
Answer each question about antidifferentiation, the constant of integration, definite integrals and the Fundamental Theorem of Calculus.
- 1.State the power rule for antidifferentiation of (for n not equal to -1).
- 2.Why does an indefinite integral always include a constant of integration + C?
- 3.For a curve that stays above the x-axis on [a, b], what does the definite integral from a to b represent?
- 4.Why does the constant of integration C not affect the value of a definite integral?
- 5.Two curves have exactly the same derivative function. How are the curves related?
- 6.Antidifferentiation is the reverse of which operation taught in the differentiation unit?
- 7.State the rule the Fundamental Theorem of Calculus gives for evaluating a definite integral.
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About this worksheet
In class: Connect every idea back to differentiation: an antiderivative is a function whose derivative is f, the +C is the family of vertical translations sharing that derivative, and the Fundamental Theorem is what links areas to antiderivatives.
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