Integration by Partial Fractions | Integrate (6x³+5x²-7)/(3x²-2x-1) | Integration Class 12
Integration by Partial Fraction | Integration (6x³+5x²-7)/(3x²-2x-1) | How to Integrate Proper-Improper Rational Function Examples | By Nitin Vairal Sir.
🔥Your Questions :🔥
1) What is Integration By Partial Fraction Method.
2) How to Integrate Proper Rational Function.
3) How to Integrate Improper Rational Function.
4) Division of polynomial equations.
5) What is Degree.
6) How to find Degree of Equation.
🔸🔸🔸🔸🔸🔸🔸🔸🔸🔸🔸🔸🔸🔸🔸🔸🔸
Student , in the previous lecture, you have studied Integration of Rational Function Theory , That means we study following points.
1) What is the rational function?
2) How many types of the rational function ?
3) What is the Proper Rational Function? And how to solve examples?
4) What is Improper Function? And how to solve examples?
5) Steps to solve examples.
Today, In this lecture we study Integration by Partial Fraction Method Examples. In this section we discuss two Integration , Proper and Improper Rational Function .
Ex.1) ∫ (6x³+5x²-7)/(3x²-2x-1)dx.
🔹🔹🔹🔹🔹🔹🔹🔹🔹🔹🔹🔹🔹🔹🔹🔹🔹
🙏 विद्यार्थी मित्रांनो, मागील लेक्चर मध्ये म्हणजे भाग 1 मध्ये आपण, Integration of Rational Function ची थेओरी अभ्यासली त्यात आपण खालील मुद्दे पाहिले आहेत.
१) रॅशनल फंक्शन म्हणजे काय ?
२) रॅशनल फंक्शन चे प्रकार किती आहेत ?
३) प्रॉपर रॅशनल फंक्शन म्हणजे काय ? आणि त्या वरील उदाहरणे कसे सोडवावे?
४) इमप्रॉपर रॅशनल फंक्शन म्हणजे काय ? आणि त्या वरील उदाहरणे कसे सोडवावे?
५) उदाहरणे सोडवण्यासाठीच्या पायऱ्या.
आज आपण या लेक्चर मध्ये इंटिग्रेशन बाय पार्शियल फ्रॅक्शन या टाईप वरील उदाहरणे अभ्यासणार आहोत.
उदा. १) ∫ (6x³+5x²-7)/(3x²-2x-1)dx.
.. तर पूर्ण व्हिडिओ बघा आणि सर्व कॉन्सेप्ट समजुन घ्या.
तर आता नितीन वैराळ सरांच्या सोप्या शब्दात इंटिग्रेशन चा पाठ समजुन घ्या आणि भरपुर मार्क्स मिळावा..😊
(टीप : कृपया आपल्याला पूर्ण टॉपिक समजण्यासाठी आधी अपलोड केलेले बेसिक व्हिडिओ नक्की पहा.) 🙏
👉Lecture Chapters :-
0️⃣ 00:00 lecture Intro.
1️⃣ 00:09 Previous Lecture Discussion.
2️⃣ 00:52 What We discuss In this Lecture.
3️⃣ 01:07 Ex. Integration (6x³+5x²-7)/(3x²-2x-1)
🔶 How to solve.(Full Detail Explanation)
🔸01:30 How to Define Function is proper or Improper ?
🔸02:23 How to find Degree of Equation.
🔸04:35 How to convert Improper rational function in to
Quotient + (Remainder)/Denominator.
🔸05:02 How to devide Denominator equation to Numerator equation.
🔸17:44 How to integrate Quotient + (Remainder)/Denominator.
🔸20:58 Integration of Improper rational function.
∫ (8x-4)/(3x²-2x-1)dx.
🔸22:51 How to factorise 3x²-2x-1
🔸27:05 How to find Value of A and B
🔸32:03 How to integrate Factories term.
🔸34:15 How to solve Integration (2x+3)
4️⃣ 37:07 Lecture Summary.
5️⃣ 42:26 Thanks.😘
🔸🔸🔸🔸🔸🔸🔸🔸🔸🔸🔸🔸🔸🔸🔸🔸🔸
Thank you for watching this video Lecture. And for all the support you are showing! 🔥
If you liked my Lecture , please like and subscribe. It motivates me a lot...☺️
And share my channel with your friends. 🙂 See you on my next video lecture !!!
🎯 Some Chapters Link 🎯
🔶Maths Part-1 :
1) Mathematical Logic : • Mathematical logic Chapter/Math 1st/Class ...
2) Matrices : • Matrices Chapter Class 12th // Full Chapte...
3) Pair Of straight Line : • Chap 4. Pair of Straight line | Maths Part...
🔶 Maths Part-2 :
1) Differentiation : • Chap 1. Differentiation | Maths Part 2nd |...
2) Application of Derivative : • Chap 2. Application of derivatives | Maths...
3) Indefinite Integration : • Indefinite Integration | Integration Chapt...
Share🔌 !! Support🔎 !! Subscribe🔔📲
👉Subscribe : / nitinexplainjuniormaths
👉Telegram Group : https://t.me/nitinmathshelp
👉 Twitter :https://twitter.com/NitinVairal3?s=17
👉 Sharechat Group:https://b.sharechat.com/okTVziZx42
📌ABOUT :
Nitin Explain Junior Maths is a YouTube Channel . Where we will find Creative Math concept and Watch Junior Education maths videos in Marathi / English language.
🙏🙏🙏🙏
#Improper_rational_function_integration
#integration_by_partial_fractions
#Indefinite_integration_class_12
#Special_integrals_examples