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Flip to reveal answersWhat does a definite integral ∫ₐᵇ f(x) dx represent (f ≥ 0)?
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All 9 Flashcards — Area under a curve
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Question
What does a definite integral ∫ₐᵇ f(x) dx represent (f ≥ 0)?
Answer
The area between the curve and the x-axis from x = a to x = b.
Question
How do you evaluate a definite integral?
Answer
Integrate to get F(x), then compute F(b) − F(a).
Question
Does a definite integral need + C?
Answer
No — the constant cancels in F(b) − F(a).
Question
What is F(b) − F(a) in words?
Answer
The antiderivative at the top limit minus the antiderivative at the bottom limit.
Question
What happens if you swap the limits?
Answer
The sign of the integral flips.
Question
How do you find an unknown limit from a given area?
Answer
Set the definite integral equal to the area and solve for the limit.
Question
∫₁³ 2x dx = ?
Answer
[x²]₁³ = 9 − 1 = 8.
Question
∫₀² x² dx = ?
Answer
[x³/3]₀² = 8/3.
Question
Indefinite vs definite integral?
Answer
Indefinite gives a function + C; definite (with limits) gives a number.
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Topic 5.5 hub
Introduction to integration
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