Differentiate F(x)=∫₀ˣ(t²+1)dt.
Use the lesson example and name the rule before calculating.
Unit 10 · Foundation Pathway
Fundamental Theorem & Antiderivatives
How does the Fundamental Theorem connect instantaneous rate with accumulated change?
Khaemenes Academy · Calculus I
Foundation Practice
Fundamental Theorem & Antiderivatives · Show reasoning, notation, intervals, units, and corrections.
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What connects derivatives and integrals?
Use the lesson example and name the rule before calculating.
Differentiate G(x)=∫₁^{x²} cos t dt.
Use the lesson example and name the rule before calculating.
Why use a dummy variable inside an accumulation integral?
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Differentiate H(x)=∫ₓ³ e^t dt.
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Find ∫(3x²−2)dx.
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Find ∫e^x dx.
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Find F if F'=2x and F(1)=5.
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Evaluate ∫2x(x²+1)³ dx.
Use the lesson example and name the rule before calculating.
Why change bounds in a definite substitution?
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Evaluate ∫₀¹ 2x e^(x²) dx.
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How is substitution verified?
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