1 Introduction To Common Fractions And Mixed Numbers 2 Addition Of Common Fractions And Mixed Numbers 3 Subtraction Of Common Fractions And Mixed Numbers 4 Multiplication Of Common Fractions And Mixed Numbers 5 Division Of Common Fractions And Mixed Numbers 6 Combined Operations Of Common Fractions And Mixed Numbers 7 Computing With A Calculator 8 Computing With A Spreadsheet 9 Introduction To Decimal Fractions 10 Rounding Decimal Fractions And Equivalent Decimal And Common Fractions 11 Addition And Subtraction Of Decimal Fractions 12 Multiplication Of Decimal Fractions 13 Division Of Decimal Fractions 14 Powers 15 Roots 16 Table Of Decimal Equivalents And Combined Operations Of Decimal Fractions 17 Computing With A Calculator 18 Computing With A Spreadsheet 19 Achievement Review—section One 20 Ratio And Propor Tion 21 Direct And Inverse Proportions 22 Introduction To Percents 23 Basic Calculations Of Percentages, Percents, And Rates 24 Percent Practical Applications 25 Achievement Review—section Two 26 Customary (english) Units Of Measure 27 Metric Units Of Linear Measure 28 Degree Of Precision, Greatest Possible Error, Absolute Error, And Relative Error 29 Tolerance, Clearance, And Interference 30 Customary And Metric Steel Rules 31 Customary Vernier Calipers And Height Gages 32 Metric Vernier Calipers And Height Gages 33 Digital Calipers And Height Gages 34 Customary Micrometers 35 Metric Vernier Micrometers 36 Digital Micrometers 37 Customary And Metric Gage Blocks 38 Achievement Review—section Three 39 Symbolism And Algebraic Expressions 40 Signed Numbers 41 Algebraic Operations Of Addition, Subtraction, And Multiplication 42 Algebraic Operations Of Division, Powers, And Roots 43 Introduction To Equations 44 Solution Of Equations By The Subtraction, Addition, And Division Principles Of Equality 45 Solution Of Equations By The Multiplication, Root, And Power Principles Of Equality 46 Solution Of Equations Consisting Of Combined Operations And Rearrangement Of Formulas 47 Applications Of Formulas To Cutting Speed, Revolutions Per Minute, And Cutting Time 48 Applications Of Formulas To Spur Gears 49 Achievement Review—section Four 50 Lines And Angular Measure 51 Protractors—simple Semicircular And Vernier 52 Types Of Angles And Angular Geometric Principles 53 Introduction To Triangles 54 Geometric Principles For Triangles And Other Common Polygons 55 Introduction To Circles 56 Arcs And Angles Of Circles, Tangent Circles 57 Fundamental Geometric Constructions 58 Achievement Review—section Five 59 Areas Of Rectangles, Parallelograms, And Trapezoids 60 Areas Of Triangles 61 Areas Of Circles, Sectors, And Segments 62 Volumes Of Prisms And Cylinders 63 Volumes Of Pyramids And Cones 64 Volumes Of Spheres And Composite Solid Figures 65 Achievement Review—section Six 66 Introduction To Trigonometric Functions 67 Analysis Of Trigonometric Functions 68 Basic Calculations Of Angles And Sides Of Right Triangles 69 Simple Practical Machine Applications 70 Complex Practical Machine Applications 71 The Cartesian Coordinate System 72 Oblique Triangles 73 Achievement Review—section Seven 74 Introduction To Compound Angles 75 Drilling And Boring Compound-angular Holes 76 Drilling And Boring Compound-angular Holes 77 Machining Compound-angular Surfaces 78 Computing Angles Made By The Intersection Of Two Angular Surfaces 79 Computing Compound Angles On Cutting And Forming Tools 80 Achievement Review—section Eight 81 Introduction To Computer Numerical Control (cnc) 82 Control Systems, Absolute Positioning, Incremental Positioning 83 Location Of Points 84 Binary Numeration System 85 Hexadecimal Numeration System 86 Bcd (binary Coded Decimal) Numeration Systems 87 An Introduction To G- And M-codes For Cnc Programming 88 Achievement Review—section Nine Chapter58: Achievement Review—section Five
Chapter Questions Section: Chapter Questions
Problem 1AR: Add, subtract, multiply, or divide each of the following exercises as indicated. a. 3718' + 8623' b.... Problem 2AR: Determine A. Problem 3AR Problem 4AR: Express 68.85 as degrees and minutes. Problem 5AR: Express 64.1420 as degrees, minutes, and seconds. Problem 6AR: Express 3723' as decimal degrees to 2 decimal places. Problem 7AR: Express 10338'43" as decimal degrees to 4 decimal places. Problem 8AR: Using a simple protractor, measure each of the angles, l through 7, to the nearer degree. It may be... Problem 9AR Problem 10AR: Write the complement of each of the following angles. a. 67 b. 1741' c. 5447' 53" Problem 11AR: Write the complement of each of the following angles. a. 41 b. 9932' c. 10303'27" Problem 12AR: Given: ABCD and FEGH . Determine the value of each angle, 1 through 10, to the nearer minute. Problem 13AR: a. Determine: (1) 1 (2) Side a b. Determine: (1) 1 (2) Side b (3) Side c c. Determine: (1) 1 (2) 2 Problem 14AR: a. Given: a=8.400 and b=9.200 . Find c. b. Given: b=90.00 mm and c=150.00 mm. Find a. Problem 15AR: Compute 1. Problem 16AR: Determine the circumference of a circle that has a 5.360-inch radius. Round the answer to 3 decimal... Problem 17AR: Determine the diameter of a circle that has a 360.00-millimeter circumference. Round the answer to 2... Problem 18AR: a. Given: CD=184 mm and CE=118 mm. Determine CF and CD. CF = CD= b. Given: FD=26 mm and CD=78 mm.... Problem 19AR: a. Given: EB=5.150. Determine AE . b. Given: AE=4.200. Determine AB. Problem 20AR: Given: Points A and E are tangent points. EB is a diameter. AE=156,CE=140, and ED=60 . Determine... Problem 21AR: a. Given: AC=110andr=4.700 Compute arc length AC to 3 decimal places. b. Given: Arc length... Problem 22AR: a. Given: Dia H=14.520 and d=8.300. Compute Dia M. b. Given: Dia M=36.900,e=15.840 , and d=12.620.... Problem 23AR Problem 24AR: a. Given: x=360 inches and y=5.10 inches. Compute Dia A to 2 decimal places. b. Given: Dia A=8.76... Problem 25AR Problem 26AR: A flat is cut on a circular piece as shown. Determine the distance from the center of the circle to... Problem 27AR: A spur gear is shown. Pitch circles of spur gears are the imaginary circles of meshing gears that... Problem 28AR: Determine the arc length from point C to point D on the template shown. Problem 29AR Problem 30AR: Determine dimension x to 3 decimal places. Problem 31AR: Refer to the drill jig shown. Determine 1. Problem 32AR Problem 33AR Problem 34AR: Lay out the template shown. Make the layout full size using construction methods. Do not use a... Problem 30AR: Determine dimension x to 3 decimal places.
Related questions
Please answer number 5, evaluate indefinite integral , put the complete solution, and box the final answer.
Transcribed Image Text: 5. Indefinite integral of sin 2x dx
Transcribed Image Text: Garcia College
Kalibo, Aklan
LECTURE NOTES IN MATH 121 (INTEGRAL CALCULUS)
INSTRUCTOR: Engr. Josefina R. Dagohoy, MEN9
NAME OF STUDENT
PROGRAM & YEAR
INDEFINITE INTEGRALS (Trigonometric Functions)
Basic Trigonometric Derivatives and their Corresponding Indefinite Integrals
sin u = cos u
du
S cos u du = sin u + C
cos u = -sin u
f sin u du =- cos u + C
du
tan u = sec²u
du
( sec u du = tan u + C
cot u = -csc²u
du
S csc?u du =- cot u + C
sec u = sec u tan uL
du
S sec u tan u du = sec u+C
csc u = -csc u cot u
du
ſ csc u cot u du = -csc u+C
Notice the way in which the functions pair off for purposes of integration. The
sin u and cos u, sec u and tan u, csc u and cot u fit well together. An integral
ring, for instance, sin u and tanu is not in appropriate form for application of simple
ration formulas. Upon meeting such an integral we first put the integrand entirely
of sin u and cos u or in terms of tan u sec u.
miprocal Identities:
Pythagorean Identities:
sin? 0+cos?0 = 1
oso e-
sin e
Cso e
1
sco 8-
1+ tan? e = sec? 0
%3D
scc 8
cos e
1+cot?0 = csc?0
%3D
cot 0-
tan 6
cot e
Even Odd Identities:
sin(-0)=-sin 6, cse(-0)= -cac @
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
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