Evaluate ∫₀² 3x² dx.
Use the lesson example and name the rule before calculating.
Unit 09 · Foundation Pathway
Accumulation, Riemann Sums & Definite Integrals
How can infinitely refined sums measure net change and accumulated quantity?
Khaemenes Academy · Calculus I
Foundation Practice
Accumulation, Riemann Sums & Definite Integrals · Show reasoning, notation, intervals, units, and corrections.
Name
Date
State the net-change principle.
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Use a left sum for f(x)=x² on [0,2] with n=2.
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How does refinement affect a Riemann estimate?
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Use a midpoint sum for f(x)=x on [0,2] with n=2.
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Use a left sum for f(x)=x² on [0,2] with n=2.
Use the lesson example and name the rule before calculating.
For an increasing function, which is typically larger: left or right sum?
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A graph has area 5 above and area 2 below the axis. Find the signed integral.
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Evaluate ∫₀² 3x² dx.
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State the net-change principle.
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If a rate is in liters/minute and dt is minutes, what are integral units?
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Why can a definite integral be negative?
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