Intergal

Let f and g be continuous functions such that ∫[0,10] of f(x)dx=21, ∫[0,10] of 1/2g(x)dx=8, and ∫[3,10] of (f(x)-g(x))dx=2. What is the value of ∫[0,3] of (f(x)-g9x))dx?

The particle moves along the x-axis. The velocity of the particle at time t is given by v(t), and the acceleration of the particle at time t is given by a(t). Which of the following gives the average velocity of the particle from time t=0 to time t=8?

(a(8)-a(0))/8

1/8∫[0,8] of v(t) dt

1/2∫[0,8] of v(t) dt

∫(sin(2x) + cos(2x))dx=

-1/2cos(2x) + 1/2sin(2x)+C

1/2cos(2x) + 1/2sin(2x)+C

2cos(2x) - 2sin(2x)+C

2cos(2x) + 2sin(2x)+C

The table below gives value of a function f and its derivative at selected values of x. If f' is continuous on the interval [-4,-1], what is the value of ∫[-4,-1] of f'(x)dx?

x	-4	-3	-2	-1
f(x)	0.75	-1.5	-2.25	-1.5
f'(x)	-3	-1.5	0	1.5

The velocity , ft/sec, of a particle moving along the x-axis is given by the function v(t)= e^t+te^t. What is the average velocity of the particle from time t=0 to time t=3?

79.342ft/sec

20.086ft/sec

40.671ft/sec

32.809ft/sec

Let f be a function such that ∫[6,12] of f(2x)dx=10. Which of the following must be true?

∫[3,6] f(t) dt= 5

�[6,12] f(t) dt= 20

�[6,12] f(t) dt= 5

�[12,24] f(t) dt= 20

What is the value of size of the subinterval when calculating a RRAM approximation of the area under f(x)=3x^2-5x+1 on [2,7] with 6 subdivisions?

1/2

3/2

5/6

Which of the following is true?

I. If f(x) is increasing on [a,b] then the left Riemann sum for ∫[a,b] of f(x) dx ia an underestimate.

II. If f(x) is concave down on [a,b], then the trapezoid approximation for ∫[a,b] of f(x) dx is an overestimate the area under the curve.

III. If f(x) is concave down on [a,b], then the midpoint Riemann sum ∫[a,b] of f(x) dx is an overestimate.

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