Unit 6 MCQ AP Calc

The graph of the function f defined on the closed interval [−2,2] is shown above. Let g be defined by g(x)=∫x0f(t)ⅆt. On which of the following intervals is the graph of g both decreasing and concave up?

(1,2)

The graph of the piecewise linear function f, which has a domain of −1≤x≤3, is shown in the figure above. What is the value of ∫3−1f(x)ⅆx ?

-1

Selected values of the twice-differentiable function g are given in the table above. What is the value of ∫30g′(x)cos2(2g(x)+1)ⅆx ?

-3.464

Which of the following limits is equal to ∫31sin(x3+2)ⅆx ?

limn→∞∑k=1nsin((1+2k/n)^3+2)2/n

ⅆⅆx(∫x2sin(t4)ⅆt)=

sin(x^4)

Which of the following is a right Riemann sum for ∫831+x√ⅆx ?

∑k=1n(4+5k/n√⋅5/n)

∫exsin(6ex+3)ⅆx=

−1/6cos(6e^x+3)+C

∫1−x2+6x−10 dx=

−tan^−1(x−3)+C

Which of the following is equivalent to ∫(2x3+1)2ⅆx ?

∫(4x^6+4x^3+1)ⅆx

limn→∞∑k=1n(√42+3k/n⋅3/n)=

∫2-5x√4ⅆx

Which of the following is equivalent to ∫e611x(2+lnx)ⅆx ?

∫2-8 1/uⅆu

Which of the following is an antiderivative of f(x)=cos(x2−5) ?

∫π-xcos(t^2−5)ⅆt

Let f be the function given by f(x)=x2e−x. It is known that ∫10f(x)ⅆx=0.160603. If a midpoint Riemann sum with two intervals of equal length is used to approximate ∫10f(x)ⅆx, what is the absolute difference between the approximation and ∫10f(x)ⅆx ?

0.003

Let g be the function defined by g(x)=∫x−1(−12+cos(t3+2t))ⅆt for 0<x<π2. At what value of x does g attain a relative maximum?

0.471

Using the substitution u=4x−3, ∫x(4x−3)10ⅆx is equivalent to which of the following?

1/16∫(u^11+3u^10)ⅆu

Which of the following is equivalent to ∫cos(4x)sin5(4x)ⅆx ?

1/4∫u^5ⅆu where u=sin(4x)

If ∫20f(x)ⅆx=4 and ∫20g(x)ⅆx=−5, then ∫20(3f(x)−g(x))ⅆx=

17

Let f be the piecewise function given above. The value of ∫80f(x)ⅆx is

2

Let f be a differentiable function such that f(1)=π2 and f′(x)=3arctan(x2−3x+2). What is the value of f(3)?

2.899

The graph of the function g on the closed interval [0,10] consists of four line segments, as shown above. Let f be the function defined by f(x)=∫x24g(t)ⅆt. What is the value of f′(3) ?

24

∫102x3−x2+2x+2x2+1 dx=

3pi/4

If h(x)=∫x3−12+t2−−−−−√ⅆt for x≥0, then h′(x)=

3x^2√2+x^6

The graph of the function f, shown above, consists of two line segments. If h is the function defined by h(x)=∫x0f(t)ⅆt for 0≤x≤6, then h′(4) is

5

∫108x−4x2−−−−−−−√ dx=

5sin^−1(x−1)+C

The continuous function f is known to be increasing for all x. Selected values of f are given in the table above. Let L be the left Riemann sum approximation for ∫101f(x)ⅆx using the four subintervals indicated by the table. Which of the following statements is true?

L=2.8 and is an underestimate for ∫1-10f(x)dx

Let f be the function given by f(x)=x2+1x√+x+5. It is known that f is increasing on the interval [1,7]. Let R3 be the value of the right Riemann sum approximation for ∫71f(x)ⅆx using 3 intervals of equal length. Which of the following statements is true?

R3=13.133 and is an overestimate for ∫1-7f(x)ⅆx

Selected values of the differentiable function h and its first derivative h′ are given in the table above. Let f be the function defined by f(x)=∫x0h(t)ⅆt. What is the least possible number of critical points for f in the interval 2≤x≤13 ?

Two