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Basic-Calculus_Q4-Module-3

Grade 12 STEM

Garry6
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Basic-Calculus_Q4-Module-3

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  1. SENIOR HIGH SCHOOL Basic Calculus Antiderivatives of Exponential & Logarithmic Functions Module 3 Quarter 4

  2. Basic Calculus Quarter 4– Module 3: Antiderivatives of Exponential & Logarithmic Functions First Edition, 2020 Republic Act 8293, section 176 states that: No copyright shall subsist in any work of the Government of the Philippines. However, prior approval of the government agency or office wherein the work is created shall be necessary for exploitation of such work for profit. Such agency or office may, among other things, impose as a condition the payment of royalties. Borrowed materials (i.e., songs, stories, poems, pictures, photos, brand names, trademarks, etc.) included in this module are owned by their respective copyright holders. Every effort has been exerted to locate and seek permission to use these materials from their respective copyright owners. The publisher and authors do not represent nor claim ownership over them. Published by the Department of Education Division of Pasig City Development Team of the Module Writer: Emma G. Gonzalvo Editors: Nenet M. Pe? ̃aranda Reviewers: Erwin C. Lugtu, Raffy D. Maga, Annie Ascotia, and Ron Robert Peca? ̃a Illustrator: Name Layout Artist: Name Management Team: Ma. Evalou Concepcion A. Agustin OIC-Schools Division Superintendent Carolina T. Rivera, Ed. D. OIC-Assistant Schools Division Superintendent Victor M. Javena, Ed D. Chief - School Governance and Operations Division Manuel A. Laguerta, Ed. D. Chief- Curriculum Implementation Division Education Program Supervisors 1. Librada L. Agon, Ed. D.,EPP/TLE 2. Liza A. Alvarez, Science 3. Bernard R. Balitao, Araling Panlipunan 4. Joselito E. Calios, English 5. Norlyn D. Conde, Ed. D., MAPEH 6. Wilma Q. Del Rosario, LRMS 7. Ma. Teresita E. Herrera, Ed. D., Filipino 8. Perlita M. Ignacio, Ph. D., ESP/SPED 9. Dulce O. Santos, Ed. D., Kinder/MTB 10. Teresita P. Tagulao, Ed. D., Mathematics Printed in the Philippines by the Department of Education – Division of Pasig City

  3. Basic Calculus SENIOR HIGH SCHOOL Module 3 Quarter 4 Antiderivatives of Exponential & Logarithmic Functions

  4. Introductory Message For the facilitator: Welcome to the Basic Calculus for Senior High School Module on Antiderivatives of Exponential & Logarithmic Functions ! This module was collaboratively designed, developed and reviewed by educators from Schools Division Office of Pasig City headed by its Officer-In-Charge Schools Division Superintendent, Ma. Evalou Concepcion A. Agustin in partnership with the Local Government of Pasig through its mayor, Honorable Victor Ma. Regis N. Sotto. The writers utilized the standards set by the K to 12 Curriculum using the Most Essential Learning Competencies (MELC) while overcoming their personal, social, and economic constraints in schooling. This learning material hopes to engage the learners into guided and independent learning activities at their own pace and time. Further, this also aims to help learners acquire the needed 21st century skills especially the 5 Cs namely: Communication, Collaboration, Creativity, Critical Thinking and Character while taking into consideration their needs and circumstances. In addition to the material in the main text, you will also see this box in the body of the module: Notes to the Teacher This contains helpful tips or strategies that will help you in guiding the learners. As a facilitator you are expected to orient the learners on how to use this module. You also need to keep track of the learners' progress while allowing them to manage their own learning. Moreover, you are expected to encourage and assist the learners as they do the tasks included in the module.

  5. For the learner: Welcome to the Basic Calculus Module on Antiderivatives of Exponential & Logarithmic Functions! The hand is one of the most symbolized part of the human body. It is often used to depict skill, action and purpose. Through our hands we may learn, create and accomplish. Hence, the hand in this learning resource signifies that you as a learner is capable and empowered to successfully achieve the relevant competencies and skills at your own pace and time. Your academic success lies in your own hands! This module was designed to provide you with fun and meaningful opportunities for guided and independent learning at your own pace and time. You will be enabled to process the contents of the learning material while being an active learner. This module has the following parts and corresponding icons: Expectation - These are what you will be able to know after completing the lessons in the module Pre-test - This will measure your prior knowledge and the concepts to be mastered throughout the lesson. Recap - This section will measure what learnings and skills that you understand from the previous lesson. Lesson- This section will discuss the topic for this module. Activities - This is a set of activities you will perform. Wrap Up- This section summarizes the concepts and applications of the lessons. Valuing-this part will check the integration of values in the learning competency. Post-test - This will measure how much you have learned from the entire module. Ito po ang parts ng module

  6. EXPECTATION Lesson: Antiderivatives of Logarithmic and Exponential Functions Learning Objective: At the end of the learning episode, you are expected to: 1.compute the general antiderivative of logarithmic and exponential functions. PRETEST Matching Type. Match the functions in Column A with their corresponding antiderivatives in Column B. Column A Column B 1.∫(??+ 3?)?? a. 4??|?| + ? 2.∫5??? b. 3??|?| + ? 3.∫3?+2?? c. 9 3? ln3+ ? 4.∫3 ??? d. 5? ln5+ ? 5.∫4?−1?? e. ??+ 3? ln3+ ?

  7. RECAP Let us recall the following differentiation formulas: a.??(??) = ?? b.??(??) = ??ln? c.??(ln?) =1 ? LESSON Exponential and logarithmic functions are used to model population growth, cell growth, and financial growth, as well as depreciation, radioactive decay, and resource consumption, to name only a few applications. In this section, we explore integration involving exponential and logarithmic functions. Theorems on Integrals yielding the Exponential and Logarithmic functions: Theorem 3.1 ∫???? = ??+ ? Example 1. ∫2???? = 2∫???? = 2??+ ? 1 2???? = 1 2∫???? =1 Example 2. ∫ 2??+ ? ?? ln?+ ?. ????,? > 0 ???ℎ ? ≠ 1. Theorem 3.2 ∫???? = 4? ??4+ ? Example 3. ∫4??? = 4? ??4+ ? Example 4. ∫4?+1?? = ∫(4?)(41)?? = 4∫(4?)?? = 4 1 ??? = ??|?| + ? Theorem 3.3 ∫?−1?? = ∫ 1 ??? = 3??|?| + ? Example 5. ∫3?−1?? = 3∫ 5 ??? = 5∫ 1 ??? = 5??|?| + ? Example 6. ∫

  8. ACTIVITIES Solve the following integrals: 1.∫7???? 4. ∫12?+1?? 2.∫(5??− 6?)?? 5. ∫ 3.∫3(5?)?? 6. ∫−3?−1?? −4 ??? WRAP–UP Need to Remember the given Theorems on Integrals yielding the Exponential and Logarithmic functions: Theorem 3.1 ∫???? = ??+ ? ?? ln?+ ?. ????,? > 0 ???ℎ ? ≠ 1. Theorem 3.2 ∫???? = 1 ??? = ??|?| + ? Theorem 3.3 ∫?−1?? = ∫ VALUING According to Bill Henson, “Adolescent is interesting. I mean all of life is interesting and all of life is transitionary. But I think there is an exponential growth physically, intellectually, emotionally and there is so much potential”. As a senior high school student, you must push yourself to show your full potential in our situation today.

  9. POSTTEST Solve the following integrals: 1. ∫−7???? 4. ∫8?+1?? −6 ??? 2. ∫(2??− 6?)?? 5. ∫ 1 2(3?)?? 3. ∫ 6. ∫−100?−1??

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