Calc U6 Part A

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

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

17

f(x)=⎧⎩⎨⎪⎪23−1for0≤x<2for2<x<3for3≤x≤8

2

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 ∫101f(x)ⅆx∫110f(x)ⅆx.

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

limn→∞∑k=1nsin((1+2kn)3+2)2n

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

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

∑k=1n(4+5kn−−−−−−√⋅5n) - has the 4 + quantity and 5/n on the right side

limn→∞∑k=1n(2+3kn−−−−−−√4⋅3n)=

∫2 to 5 4√xⅆx

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

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

3x2 sqrt (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

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 ∫71f(x)ⅆx∫17f(x)ⅆx.

ⅆⅆx(∫x2sin(t4)ⅆt)=

sin(x4) - x to the fourth