REKAYASA IDE Applied Definite Integrals in Calculating Area, Volume, Force, and Surface Area.

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REKAYASA IDE

Applied Definite Integrals in Calculating Area, Volume, Force, and Surface Area.

Supporting lecturer : Sudianto Manullang, S. Si., M. Sc

Oleh :

Melly Abdellina Siboro (4221121007) Nadya Aidilla F. Tanjung(4221121014)

PHYSICS EDUCATION S1 STUDY PROGRAM FACULTY OF MATH AND SCIENCE

MEDAN STATE UNIVERSITY

2022

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Foreword

We thank God Almighty, because of His blessings and gifts we were able to complete the RI (Idea Engineering) assignment in Integral Calculus course. We would like to thank Mr.

Sudianto Manullang, S. Si., M. Sc. as a lecturer in this course who has provided guidance to us in compiling this RI. We expect constructive criticism and suggestions for the perfection of this work. Finally, we thank you. Hopefully it can be useful and can add to our knowledge.

Medan, 12 November 2022

Group 8.

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Table of Contents Cover

Foreword

Table of Contents Chapter I Preface

1.1 Background 1.2 Purpose 1.3 Benefit

Chapter II General Framework Chapter III New Idea

Chapter IV Conclusions and Recommendations 5.1 Conclusions

5.2 Suggestion

Bibliography

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Chapter I Preface 1.1 Background

Calculus (Latin: calculus, meaning "little stone", to calculate) is a branch of mathematics that includes limits, derivatives, integrals, and infinite series. Calculus is the science of change, just as geometry is the science of shapes and algebra is the science of working to solve equations and their applications. Calculus has wide applications in the fields of science, economics, and engineering; and can solve various problems that cannot be solved by elementary algebra.

In studying the calculus material, students experienced many obstacles due to several aspects, namely because at the time of giving calculus questions, the questions provided were very complicated and the solutions were long. Then. students are also sometimes less careful in studying the calculus material

The following will discuss the problems faced by students in understanding calculus material, especially regarding the improper integral calculus course.

1.2 Purpose

So that students are able to find the best solution to solve problems related to integral calculus courses, especially in certain integral application materials measuring area, volume, force, and surface area easily.

1.3 Benefit

Students can solve problems related to certain integral application materials to calculate area, volume, force, and surface area very well and effectively and use the fastest solutions to solve these problems.

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Chapter II General Framework 2.1 Existing Alternative Methods

There are 2 methods that we can use to calculate the volume of rotating objects using integrals, namely: disc method and Cylinder ring method.

1. Disc Method

based on the formula volume = area of the base x height of the base area. here is always a circle, then the area of the base = r² (where r is the radius of rotation) is used if the selected cross section is perpendicular to the axis of rotation

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2.

Cylinder ring method.

According to the understanding that if an area is rotated about a certain axis. A rotating object will be formed with a volume equal to the area multiplied by the circumference of the rotation. Due to the circumference of the circle = 2r, if the area of the rotated field

= A , then volume = used if the cutting rod is parallel to the axis of rotation.

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Chapter III

New Idea

Explanation of the description of the new idea offered complete with drawings or flowcharts.

The engineering idea that we created is about a quick and easy way to calculate the area and volume of rotating objects.

The following are some steps in working on questions regarding rotary objects along with quick and easy ways to do them.

Next, determine the area and volume : 1. Solve ^x³^^x²^⁶^x^⁰

2. To find the intersection points, solve ^x^{ }⁴ ^x²^²

3. slice vertically ^{ }^A ^_



^x²^{  }²

 ^{ }

^x ^_^{ }^x



^x²^{  }^x ²



^x

4. slice vertically ^{ }^A



^x²^{ }¹



^x

Answer :

1. Solve ^x³^^x²^⁶^x^⁰ Manually : ^{x x}



²^{ }^x ⁶



^⁰

^{x x}



^^{2 (}



^x^{ }^{3) 0}

^x^{ }^{2, 03} Slice vertically :



³ ²



1 6

A x x x

   



³ ²

 

³ ²



2 6 6

A x x x x x x x x

          

1 2

A A A

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   

0 3 2 3 3 2

2 6 0 6

A x x x dx x x x dx





   



  

0 3

4 3 2 4 3 2

2 0

1 1 1 1

3 3

4 3 4 3

A x x x x x x



   

        

8 81

0 4 12 9 27 0

3 4

A          

16 63 3 4 A 

253 A 12

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Chapter IV

Conclusions and Recommendations 5.1 Conclusions

There are so many obstacles or problems faced by many people. especially for students in understanding and absorbing material related to certain integral applications by determining area, volume, force, and surface area. Various methods can be used by students to make it easier for students to solve problems related to certain integral application materials. However, students must be able and understand the material studied well and maximally. Students can also add insight from the internet and so on so that their knowledge of how to determine the force, volume, and surface area of objects is obtained.

5.2 Suggestion

We hope that through this paper, students are increasingly interested in

learning more about this particular integral material and are able to complete the

material presented in a fast way so that the solution to the problem can be

solved very easily.

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Bibliography

Edwin, V. D. (2008). CALCULUS PREFACE IX. New York: SPRINGER.

Thomas, G. B. (2018). Thomas' Calculus. California: Library Of Congress.