AP Calculus AB 6.6 Applying Properties of Definite Integrals - MCQs - Exam Style Questions
No-Calc Question
The function \(f\) is defined for \(-2\le x\le 5\), and the graph of \(y=f(x)\) shown consists of three line segments. What is the value of \(\displaystyle\int_{-2}^{5}\big(f(x)+1\big)\,dx\) ?
(A) \(-10\)
(B) \(-9\)
(C) \(-3\)
(D) \(17\)
▶️ Answer/Explanation
Split the integral: \(\displaystyle\int_{-2}^{5}f(x)\,dx+\int_{-2}^{5}1\,dx\).
From areas of the three line segments in the graph, \(\displaystyle\int_{-2}^{5}f(x)\,dx=-10\).
Also \(\displaystyle\int_{-2}^{5}1\,dx=5-(-2)=7\).
Sum: \(-10+7=-3\).
✅ Answer: (C)