Mr. Orchard’s Math 142 WIR
6.1-6.3
1. Find the most general antiderivatives for the following functions:
(a) f 0 (x) = 8x9
(b) g 0 (x) = 6x + 9x7 + 2
(c) k 0 (x) =
6
u2
(d) h0 (x) =
8+u2
u
+
3
u
Week 10
Mr. Orchard’s Math 142 WIR
6.1-6.3
2. Evaluate the following indefinite integrals.
R 2
(a)
+ 4x34 − x17 dx
x
(b)
R
(c)
R 6e−x +14 (d)
R
(t5 − 4et ) dt
e−x
dx
(6x − 10)12 dx
Week 10
Mr. Orchard’s Math 142 WIR
6.1-6.3
3. Use u-substitution to evaluate the following indefinite integrals:
R
(a) e−9x dx
(b)
R
3x7 (x8 + 3)9 dx
(c)
R
x5
dx
x6 +4
(d)
R
(6x2 − 9)e6x
3 −27x
dx
Week 10
Mr. Orchard’s Math 142 WIR
6.1-6.3
4. Find f (x) given the following information:
(a) f 0 (x) = 12x2 + 8x + 4, f (2) = 58
(b) f 0 (x) =
(ln(x))48
,
x
(c) f 0 (x) =
x
,
x2 +3
(d) f 0 (x) =
10e x
x2
f (1) = 10
f (2) = 0
−2
, f (−2) = 10 − 5e
Week 10
Mr. Orchard’s Math 142 WIR
6.1-6.3
Week 10
5. An object travles with velocity v(t) = (t − 1)2 + 1. Using n = 3 and equal subintervals,
estimate the distance traveled by the object on the interval [0, 3] with a right-hand sum.
6. An object travels at a velocity given by v(t) = t2 − 2t + 2 feet per second. Using n = 5
and equal subintervals, find the following estimations for the distance the object traveled
on the interval [0, 1].
(a) Upper bound approximation
(b) Lower bound approximation
Mr. Orchard’s Math 142 WIR
6.1-6.3
Week 10
7. During regular intervals the Millenium Falcon’s speed was calculated during the Kessel
Run. Han Solo (the pilot) steadily increased his speed throughout the flight. The
information is summarized in the chart below. Use this chart to estimate the distance
Han Solo flew during this instance of the Kessel Run, with n = 8 equal subintervals and
a right hand sum.
t (in seconds)
v(t) (in parsecs per second)
0
0
2
0.45
4
0.53
6
0.66
8
0.78
10
0.80
12
0.82
14
0.83
16
0.88
Mr. Orchard’s Math 142 WIR
6.1-6.3
Week 10
8. An object has a velocity v(t) = 2t + 50 feet per second. Use n = 6 and equal subintervals
to compute the following approximations of the distance the object traveled starting one
second after it starts and ending 12 seconds later.
(a) Left-hand sum approximation
(b) Right-hand sum approximation
(c) Average of the two sums
Mr. Orchard’s Math 142 WIR
6.1-6.3
Week 10
9. Speedometer readings (in feet per second) for a motorcylce at 12-second intervals are
given in the table below:
t
v(t)
0
32
12
28
24
25
36
22
48
24
60
28
(a) Estimate the distance traveled by the motorcycle during this time using a left hand
sum with n = 5.
(b) Estimate the distance traveled by the motorcycle during this time using a right
hand sum with n = 5.