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AP Calculus BC Flashcards: Integrating Vector Valued Functions

Study Integrating Vector Valued Functions in AP Calculus BC with focused flashcards that help you recognize the idea, recall the key rule, and apply it in practice-style prompts.

QUESTION

Evaluate the integral r(t)=(t t2)\textbf{r}(t) = \begin{pmatrix} t \ t^2 \end{pmatrix} over [1,2][1, 2].

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ANSWER

(32 73)\begin{pmatrix} \textstyle\frac{3}{2} \ \textstyle\frac{7}{3} \end{pmatrix}. Integrate tt to get 32\frac{3}{2} and t2t^2 to get 73\frac{7}{3} over [1,2][1,2].

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AP Calculus BC: Parametric, Polar, and Vector Functions

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This deck focuses on Integrating Vector Valued Functions, giving you a quick way to review the definitions, rules, and examples that matter most for AP Calculus BC.

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Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Practice questions

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A particle's acceleration is a⃗(t)=⟨6t, −4⟩\vec a(t)=\langle 6t,\,-4\rangle with v⃗(0)=⟨1,2⟩\vec v(0)=\langle 1,2\rangle; find v⃗(t)\vec v(t).
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