AP Calculus BC : 6.5 Interpreting the Behavior of Accumulation Functions Involving Area- Exam Style questions with Answer- MCQ

Question

The graph of y  = ( fx) is shown in the figure above. If\( A_{1}\) and \(A_{2}\) are positive numbers that represent the areas of the shaded regions, then in terms of \( A_{1}\) and \(A_{2}\),
\(\int_{-4}^{4}f(x)dx-2\int_{-1}^{4}f(x)dx=\)

(A) \(A_{1}\)                                              (B) \(A_{1}-A_{2}\)                                         (C) \(2A_{1}-A_{2}\)                         (D) \(A_{1}+A_{2}\)                                     (E)  \(A _{1}+A_{2}\)

Answer/Explanation

Ans:C\D

 

Question

The area of the shaded region in the figure above is represented by which of the following integrals?

(A)\(\int_{a}^{c}\left ( |f(x)|-g(x) |\right )dx\)
(B)\(\int_{b}^{c} f(x)dx-\int_{a}^{c}g(x)dx\)
(C)\(\int_{a}^{c}(g(x)-f(x))dx\)
(D)\(\int_{a}^{c}(f(x)-g(x))dx\)
(E)\(\int_{a}^{b}(g(x)-f(x))dx+\int_{b}^{c}(f(x)-g(x))dx\)

Answer/Explanation

Ans:D

 

Question

Which of the following represents the area of the shaded region in the figure above?

(A) \(\int_{c}^{d}f(y)dy\)                     (B)\(\int_{a}^{b}(d-f(x))dx \)                              (C)\(f'(b)-f'(a)   \)                         (D)\( (b-a)[f(b)-f(a)] \)                                      (E)\((d-c)[f(b)-f(a)]\)

Answer/Explanation

Ans:B

Summing pieces of the form: (vertical). (small width), vertical = (d− f(x)), width = \(\Delta x\)

Question

The function f is continuous on the closed interval [ 0, 6] and has the values given in the table above. The trapezoidal approximation for\( \int_{0}^{6}f(x)\) dx found with 3 subintervals of equal length is 52. What is the value of k ?
(A) 2                (B) 6                   (C) 7                     (D) 10                    (E) 14

Answer/Explanation

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