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Flip to reveal answersWhat is ∫ₐᵃ f(x) dx?
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All 9 Flashcards — Definite integrals
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Question
What is ∫ₐᵃ f(x) dx?
Answer
0 — a zero-width interval has zero area.
Question
What happens if you swap the limits of a definite integral?
Answer
The sign flips: ∫ₐᵇ f = −∫_b^a f.
Question
State the interval-splitting property.
Answer
∫ₐᵇ f + ∫_b^c f = ∫ₐ^c f.
Question
How do you evaluate a definite integral?
Answer
Find an antiderivative F, then compute F(b) − F(a).
Question
What mode should the GDC be in for trig integrals?
Answer
Radian mode (the limits are in radians).
Question
∫₀^(π/2) cos x dx = ?
Answer
[sin x]₀^(π/2) = 1.
Question
What does the integral of a rate of change give?
Answer
The total (accumulated) change over the interval.
Question
How do you find the amount at time b from a rate?
Answer
amount(b) = amount(a) + ∫ₐᵇ (rate) dt.
Question
∫₀^π sin x dx = ?
Answer
[−cos x]₀^π = 2.
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Full study notes for Definite integrals
Topic 5.11 hub
Definite integrals & areas
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