#6. Evaluate.
1
a)
x ( arctan ( x ) ) x
0
The first step I took was to cancel out the d/dx and the dx. One asked you to take the derivative and the
other asks for antiderivative. You end up in your original place.
Next, is to plug in the integral numbers
8. b
All we do for this part is change the distance that the water is lifted to the top of the tank. In this case,
the integral for the work would change to:
After plugging this integral in your calculator, you should get
313,656 ft-lbs
Or BY HAND:
After
4.2 Homework - Answers
1
1. A slope field for the differential equation = (1 4 2 ) is shown.
a) Sketch the graphs of the solutions that satisfy the following initial conditions:
i) (0) = 1
ii) (0) = 1
iii) (0) = 3
iv) (0) = 3
b) Find all equilibrium solut
1.3 Riemann Sums - Answers
For problems 1 through 4 calculate the sum.
1. 4=0 21 =
31
2
2. 8=2 3 = 105
3. 8=1
5
2
= 2
4. 5=1( 2 + 2) = 65
For Problems 5 through 8 write the sum using sigma notation. Multiple answers are possible, Ive given
one option for
1.2 The Area and Distance Problems - Answers
1. A car comes to a stop nine seconds after the driver applies the brakes. While the brakes are on the
velocities are recorded every three seconds in the table below.
a) Give lower and upper estimates for the d
For problems 1 through 4 calculate the sum.
5
4.
( x 2+2)
x=1
- The first thing we should notice is that the numbers that were using is 1 through 5.
1
2
3
4
5
2
- Next we use the equation that is given ( x +2 ), and we plug in the numbers (1- 5) into x.
Name: -
_ Score:
Math 152 - Skills Test
To receive credit. dear and correct work must be show for each problem. All answers shbuld be exact (no
decimals). Calculators may not be used.
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2.2 DAY 1 #2
5t
t t
Steps:
1) We need to identify what the parts are (u, v, du, dv)
5t
U=t
v=
Du= dt
dv=
5
5 t t
2) now we input all those terms into the formula:
uv =uv Vu
5 t
5 t
t
(t) ( 5
5
( )
3) Now you see the (
(t )
(t )
5 t
t , we should bring
APEX
C
II
Version 2.0
Authors
Gregory Hartman, Ph.D.
Department of Applied Mathema cs
Virginia Military Ins tute
Brian Heinold, Ph.D.
Department of Mathema cs and Computer Science
Mount Saint Marys University
Troy Siemers, Ph.D.
Department of Applied Math
die?) Uracil
Name. Kggj . Math 152 _ Exam 2 Smelgj/
To receive full credit, cle and correct work as discussed in class must be shown for each problem unless otherwise indicated. Work on scratch paper will not be
graded. Onl answers to a catio m ' n d 'mal
THE METHOD OF U-SUBSTITUTION
The following problems involve the method of u-substitution. It is a method for
finding antiderivatives. We will assume knowledge of the following well-known,
basic indefinite integral formulas :
1.
2.
3.
4.
, where a is a con