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Calculus AB Flashcards

7 cards from real AP practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

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  1. What is ∫(3x² + 2x − 5)dx?

    Answer: x³ + x² − 5x + C

    Integrating term by term with the reverse power rule yields x³ + x² − 5x + C.

  2. What is ∫₀² 2x dx?

    Answer: 4

    The antiderivative is x²; evaluated from 0 to 2 gives 4 − 0 = 4.

  3. According to the Fundamental Theorem of Calculus Part 1, d/dx[∫_a^x f(t) dt] equals which of the following?

    Answer: f(x)

    FTC Part 1 states that differentiating a variable-upper-limit integral returns the integrand evaluated at the upper limit, f(x).

  4. What is ∫e^x dx?

    Answer: e^x + C

    The function e^x is its own antiderivative, so ∫e^x dx = e^x + C.

  5. Using u-substitution, what is ∫2x(x² + 1)⁴ dx?

    Answer: (x² + 1)⁵/5 + C

    Let u = x² + 1, du = 2x dx; the integral becomes ∫u⁴ du = u⁵/5 + C = (x² + 1)⁵/5 + C.

  6. What is the area bounded by f(x) = sin(x) and the x-axis from x = 0 to x = π?

    Answer: 2

    ∫₀^π sin(x) dx = [−cos(x)]₀^π = (−cos π) − (−cos 0) = 1 + 1 = 2.

  7. Which technique is most appropriate for evaluating ∫x·eˣ dx?

    Answer: Integration by parts

    Integration by parts (∫u dv = uv − ∫v du) is designed for products of algebraic and transcendental functions like x·eˣ.