AP Calculus BC Unit 6 practice questions: Integration and Accumulation of Change
8 original multiple-choice questions on AP Calc BC Unit 6, integration and accumulation of change. Answer each one in your browser and read the explanation, then review the key ideas below.
Question 1 of 8
Find ∫ x·eˣ dx.
Question 2 of 8
Find ∫ 1/(x(x + 1)) dx.
Question 3 of 8
Evaluate the improper integral ∫ from 1 to ∞ of 1/x² dx.
Question 4 of 8
Evaluate ∫ from 0 to 2 of 3x² dx.
Question 5 of 8
What is d/dx of ∫ from 0 to x² of cos t dt?
Question 6 of 8
Find ∫ x/(x² + 1) dx.
Question 7 of 8
Using a right Riemann sum with 2 equal subintervals, estimate ∫ from 0 to 2 of x² dx.
Question 8 of 8
Find ∫ cos(2x) dx.
Key ideas in Unit 6
- A definite integral is the limit of Riemann sums and gives net accumulated change. Know left, right, midpoint and trapezoidal approximations.
- The Fundamental Theorem of Calculus: ∫ from a to b of f(x) dx = F(b) − F(a), and d/dx ∫ from a to g(x) of f(t) dt = f(g(x))·g′(x).
- u-substitution reverses the chain rule; remember to change the limits or substitute back.
- BC adds integration by parts (∫ u dv = uv − ∫ v du), partial fractions with linear factors, and improper integrals evaluated as limits.
More AP Calc BC practice
← Unit 5: Analytical Applications of Differentiation
Unit 7: Differential Equations →
The full AP Calculus BC practice test, all units
Studying from your own notes? Turn them into a practice quiz, a study guide or flashcards.