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Flip to reveal answersWhat does a negative definite integral tell you about the region?
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All 9 Flashcards — Area between curves
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Question
What does a negative definite integral tell you about the region?
Answer
The region lies below the x-axis; the area is the magnitude of the integral.
Question
Is area ever negative?
Answer
No — take the absolute value of a negative integral for the area.
Question
How do you find the area between two curves?
Answer
∫ₐᵇ (top − bottom) dx, where 'top' is the upper curve.
Question
How do you decide which curve is the 'top'?
Answer
Test an x-value between the limits (or sketch) to see which has greater y.
Question
How do you find the limits for an enclosed region between two curves?
Answer
Solve top = bottom to find the intersection x-values.
Question
Area between a curve and the x-axis when it dips below?
Answer
Split at the x-intercepts and add the magnitudes (or take |∫|).
Question
Area between y = x and y = x² on [0,1]?
Answer
∫₀¹ (x − x²) dx = 1/6.
Question
Why does (top − bottom) work even below the axis?
Answer
Subtracting the lower curve measures the vertical gap, which is always positive.
Question
First step for an enclosed area between two curves?
Answer
Find the intersection points (solve top = bottom) for the limits.
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Topic 5.11 hub
Definite integrals & areas
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