antiderivatives, substitution and basic integration techniques

Review antiderivatives, substitution and basic integration techniques for AP Calculus AB and try 2 free AP-style practice questions. 27 questions on this topic in AP Calculus AB · Unit 6 · Integration and Accumulation of Change.

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Question 1

Suppose the rate of change of Avalon's population is $P'(t) = 6t + 8$ (thousands per year) for $t \ge 0$ , and $P(0) = 50$ . What is $P(5)$ ?

Question 2

$\int_0^4 12x\sqrt{x^2+9}\,dx =$

25 more questions on this topic

Full practice for AP Calculus AB · Unit 6 · Integration and Accumulation of Change: timed tests, step-by-step explanations for every answer, and AI grading for free-response questions.

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Answer, then see why

The price of gasoline rises 10% and the quantity demanded falls 5%. What happens to total revenue?

Not quite. The answer is B.

Why the other options are wrong

AI grading for free-response

Write your FRQ answer and get it scored point by point against the AP rubric, with the line from your answer that earned or missed each point.

Question 13 / 4 pts

Part a1 / 1 pts

Point 1: Earned

94% sure

Reason: Correctly identifies demand for gasoline as inelastic.

Evidence: "The price of gasoline rises and the quantity falls only a little."

Part b2 / 3 pts

Point 1: Earned

91% sure

Reason: Graph shows relatively inelastic demand.

Evidence: Draws a steep demand curve.

Point 2: Earned

88% sure

Reason: Correct new equilibrium price.

Evidence: Shifts supply left, P1 → P2.

Point 3: Not earned

82% sure

Reason: With inelastic demand, a price increase raises total revenue.

Evidence: "Revenue goes down."

Antiderivatives, substitution and basic integration techniques: AP Calculus AB Practice Questions | S&D Academy