AP Calculus BC : 6.1 Exploring Accumulations of Change- Exam Style questions with Answer- MCQ

Question

The graph of a piecewise-linear function f, for \(-1 \leq x \leq 4\), is shown above. What is the value of \(\int_{-1}^{4} f(x) dx\)?

(A) 1
(B) 2.5
(C) 4
(D) 5.5
(E) 8

▶️ Answer/Explanation

Solution

1. Break the integral into two parts based on the graph’s behavior:

\(\int_{-1}^{4} f(x) dx = \int_{-1}^{2} f(x) dx + \int_{2}^{4} f(x) dx\)

= Area of trapezoid(1) – Area of trapezoid(2) = 4 -1.5= 2.5

✅ Answer: B) 2.5

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