Evaluate ∫(x²+2x)dx.
Generalize, analyze an edge case, or defend the result without relying on technology.
Unit 11 · Extended Pathway
Integration Methods & Numerical Analysis
How do structure, approximation, and error analysis guide the evaluation of integrals?
Khaemenes Academy · Calculus I
Extended Practice
Integration Methods & Numerical Analysis · Show reasoning, notation, intervals, units, and corrections.
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Compare exact and decimal answers.
Generalize, analyze an edge case, or defend the result without relying on technology.
Evaluate ∫(1/x)dx for x>0.
Generalize, analyze an edge case, or defend the result without relying on technology.
Name a reliable final check.
Generalize, analyze an edge case, or defend the result without relying on technology.
Why simplify (x²+x)/x before integrating?
Generalize, analyze an edge case, or defend the result without relying on technology.
Evaluate ∫(1/x)dx for x>0.
Generalize, analyze an edge case, or defend the result without relying on technology.
Compare exact and decimal answers.
Generalize, analyze an edge case, or defend the result without relying on technology.
Evaluate ∫x e^x dx.
Generalize, analyze an edge case, or defend the result without relying on technology.
For [0,4] with n=4, find Δx.
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.
Evaluate ∫(1/x)dx for x>0.
Generalize, analyze an edge case, or defend the result without relying on technology.
Name a reliable final check.
Generalize, analyze an edge case, or defend the result without relying on technology.