Evaluate ∫₀² 3x² dx.
Generalize, analyze an edge case, or defend the result without relying on technology.
Unit 09 · Extended Pathway
Accumulation, Riemann Sums & Definite Integrals
How can infinitely refined sums measure net change and accumulated quantity?
Khaemenes Academy · Calculus I
Extended Practice
Accumulation, Riemann Sums & Definite Integrals · Show reasoning, notation, intervals, units, and corrections.
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Date
State the net-change principle.
Generalize, analyze an edge case, or defend the result without relying on technology.
Use a left sum for f(x)=x² on [0,2] with n=2.
Generalize, analyze an edge case, or defend the result without relying on technology.
How does refinement affect a Riemann estimate?
Generalize, analyze an edge case, or defend the result without relying on technology.
Use a midpoint sum for f(x)=x on [0,2] with n=2.
Generalize, analyze an edge case, or defend the result without relying on technology.
Use a left sum for f(x)=x² on [0,2] with n=2.
Generalize, analyze an edge case, or defend the result without relying on technology.
For an increasing function, which is typically larger: left or right sum?
Generalize, analyze an edge case, or defend the result without relying on technology.
A graph has area 5 above and area 2 below the axis. Find the signed integral.
Generalize, analyze an edge case, or defend the result without relying on technology.
Evaluate ∫₀² 3x² dx.
Generalize, analyze an edge case, or defend the result without relying on technology.
State the net-change principle.
Generalize, analyze an edge case, or defend the result without relying on technology.
If a rate is in liters/minute and dt is minutes, what are integral units?
Generalize, analyze an edge case, or defend the result without relying on technology.
Why can a definite integral be negative?
Generalize, analyze an edge case, or defend the result without relying on technology.