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.
Read the first 7 Calculus AB flashcards as text
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.
What is ∫₀² 2x dx?
Answer: 4
The antiderivative is x²; evaluated from 0 to 2 gives 4 − 0 = 4.
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).
What is ∫e^x dx?
Answer: e^x + C
The function e^x is its own antiderivative, so ∫e^x dx = e^x + C.
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.
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.
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.