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Stewart_Calc_7ET ch07sec07
MULTIPLE CHOICE
1. Use the Trapezoidal Rule to approximate the integral with answers rounded to four decimal
places.
a.
0.2029
b.
0.1088
c.
0.1163
d.
0.2326
2. Use Simpson’s Rule to approximate the integral with answers rounded to four decimal
places.
a.
2.0076
b.
2.9504
c.
2.6098
d.
2.2955
3. Use Simpson’s Rule to approximate the integral with answers rounded to four decimal
places.
a.
4.0689
b.
3.3296
c.
2.9599
d.
3.6993
4. Use the Midpoint Rule to approximate the given integral with the specified value of n.
Compare your result to the actual value. Find the error in the approximation.
a.
b.
c.
0.00008
d.
1.00008
e.
5. Use the Trapezoidal Rule to approximate the integral with answers rounded to four decimal
places.
a.
0.8528
b.
0.9842
c.
0.4921
d.
0.4695
6. Use Simpson’s Rule to approximate the integral with answers rounded to four decimal
places.
a.
2.2028
b.
2.7519
c.
3.0265
d.
2.4774
NUMERIC RESPONSE
1. Estimate the area of the shaded region by using the Trapezoidal Rule with . Round the
answer to the nearest tenth.
2. Use the Trapezoidal Rule to approximate for . Round the result to four
decimal places.
SHORT ANSWER
1. Use (a) the Trapezoidal Rule and (b) Simpson’s Rule to approximate the integral to four
decimal places. Compare your results with the exact value.
2. Eight milligrams of a dye are injected into a vein leading the an individual’s heart. The
concentration of dye in the aorta (in milligrams per liter) measured at 2-sec intervals is
shown in the accompanying table. Use Simpson’s Rule with and the formula
to estimate the person’s cardiac output, where D is the quantity of dye injected in
milligrams, is the concentration of the dye in the aorta, and R is measured in liters per
minute. Round to one decimal place.
t
0
2
4
6
8
10
12
14
16
18
20
22
24
C(t)
0
0
2.6
6.3
9.7
7.5
4.5
3.5
2.2
0.6
0.3
0.1
0
3. Find a bound on the error in approximating the integral using (a) the Trapezoidal Rule and
(b) Simpson’s Rule with n subintervals.
4. Find a bound on the error in approximating the integral using (a) the Trapezoidal Rule and
(b) Simpson’s Rule with n subintervals.
5. Find a bound on the error in approximating the integral using (a) the Trapezoidal
Rule and (b) Simpson’s Rule with subintervals.
6. A body moves along a coordinate line in such a way that its velocity at any time t, where
, is given by
.
Find its position function if it is initially located at the origin.
7. Find a bound on the error in approximating the integral using (a) the Trapezoidal Rule and
(b) Simpson’s Rule with n subintervals.
