The rate of water flow R(t) can be estimated by W(t) = ln(t2 + 7). Use W(t) to approximate the average rate of water flow during the 8-hour time period. Indicate units of measure.

Which of the following definite integrals could be used to calculate the total area bounded by the graph of y = sin(x), the x-axis, x = 0, and x = π (4 points)
 
the integral from 0 to pi of the sine of x, dx
the integral from 0 to pi of the negative sine of x, dx
2 times the integral from 0 to pi of the sine of x, dx
one half times the integral from 0 to pi of the sine of x, dx
2.  Suppose the integral from 2 to 8 of g of x, dx equals 13 , and the integral from 6 to 8 of g of x, dx equals negative 3 , find the value of 2 plus the integral from 2 to 6 of g of x, dx . (4 points)
 
16
18
8
32
3.  Evaluate the integral the integral from 0 to 2 of the absolute value of x, dx . (4 points)
 
-2
0
2
4
4.  Use your graphing calculator to evaluate to three decimal places the value of the integral from negative 1 to 1 of the product 2 and the square root of 1 minus x squared over 2, dx . (4 points)
 
3.771
3.636
1.571
1.111
5.  the integral from 3 to 5 of 1 divided by the quantity x plus 1, dx is equal to the integral from 4 to 6 of 1 divided by u, du (4 points)
 
True
False
1.  Find the average value of f(x)=e2x over the interval [2, 4]. (4 points)
 
1463.18
731.59
1517.78
23.60
2.  Find the velocity, v(t), for an object moving along the x-axis if the acceleration, a(t), is a(t) = 2t + sin(t) and v(0) = 4. (4 points)
 
v(t) = t2 + cos(t) + 3
v(t) = 2 + cos(t) + 1
v(t) = t2 – cos(t) + 5
v(t) = t2 + sin(t) + 4
3.  Find the distance, in feet, a particle travels in its first 4 seconds of travel, if it moves according to the velocity equation v(t)= -t2 + 4 (in feet/sec). (4 points)
 
55 over 3
16 over 3
16
12
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