Dr Rizwan

https://youtu.be/SIp9Ii5YOHU

​
Exercise 5.1 Class 12 math || NBF New Book 2025 || ex 5.1 class 12 maths NBF || Displacement-Time and Velocity-Time Graphs || by Dr Rizwan

In this video, we solve Exercise 5.1 from Class 12 Mathematics, Chapter/unit 05 of National Book Foundation (NBF) as Federal Textbook Board Islamabad Pakistan. This book is based on National curriculum of Pakistan 2022-23.

We provide step-by-step solutions with clear explanations to help you excel in board exams and achieve an A+ grade. During our lectures, we highlight important questions with a high probability of appearing in the exam. Our teaching style focuses on building strong concepts—not just preparing you for top grades, but also equipping you for university entrance tests after your second year.

📌 Topics Covered:
- Complete solution of Exercise 5.1 Class 12 Math
- displacement-time graph
- acceleration-time graph
- velocity from displacement-time graphs
- acceleration and distance from velocity-time graph
- Shortcuts for board exams

🎯 Best For:
✔️ Class 12 Mathematics Federal Board (FBISE)
✔️ Mechanic/Physics Students
✔️ ICS / Pre-Engineering Students
✔️ Entry Test Preparation: NET (NUST), UET, FAST, GIKI, PIEAS, COMSATS, LUMS SSE

💡 Why Watch This Video?
This lesson will help you understand the concepts clearly, save time in exams, and score higher marks.

💡 Why Subscribe to our YouTube Channel Dr Rizwan?
📚 Learn from a PhD with 10+ years’ experience
🧠 Strong concept building, not just exercise solving
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📊 Graphs & diagrams for clear understanding
🎯 Focus on exams + university entrance tests
🔍 High-probability exam questions highlighted

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https://youtu.be/Ak2XhJ4GQ4Y

Assalamualaikum dear students! 👋
Agar aap FSc Part 2 Mathematics (Federal Board) ke National Book Foundation – Chapter 3: Integration ka Exercise 3.4 – Integration by Parts easily samajhna chahte hain, toh yeh video aap ke liye complete solution ke saath tayar ki gayi hai ✅

Integration by parts aik aisi technique hai jo 2 functions ke product ka integral nikaalne ke liye istemal hoti hai. Yeh asal mein product rule (jo hum differentiation mein use karte hain) ka ulta tareeqa hai. Is lecture mein hum Integration by Parts ka concept basic to advanced level tak explain karenge. Har question ka step-by-step solution, proper formula use, aur real exam tips share kiye gaye hain. Video Urdu mein hai taake har student asaani se seekh sake.

📌 Topics Covered in This Lecture:
🔹 What is Integration by Parts (with derivation)
🔹 Integration by Parts Formula: ∫1st2nd dx = 1st ·∫ 2nd dx− ∫[ ∫ 2nd dx . d/dx (1st) ] dx
🔹 How to choose 1st and 2nd (ILATE tip explained)
🔹 Solving integrals involving inverse trigonometric, logarithmic, algebraic, exponential & trigonometric functions
🔹 Solving complex integrals using repeated integration by parts
🔹 Full solution of Exercise 3.4 – Federal Board New Syllabus 2025
🔹 Most common mistakes in Integration by Parts
🔹 Extra tricky questions for practice (beyond textbook)
🔹 Best and easiest way to learn integration by parts

🕒 Time Code – Exercise 3.4 Breakdown
00:00 – Introduction and Overview
06:11 – What is Integration by Parts - Easy to learn formula
12:52 – How to choose first function and second function
17:38 – ILATE Tip – Choosing first and second function
25:45 – Question 01 - integral lnx dx
30:17 – Question 02 - integral (lnx)^2 dx
34:48 – Question 03 - integral sin(lnx) dx (very important)
42:11 – Question 08 - integral ln(2x+3) dx (very important)
47:30 – Question 18 - integral lnx/ under root(x) dx (very important)
51:49 – Question 15 - integral ln(x+under root(x^2+1) dx (very important)
1:00:09 – Question 11 - integral cos^-1 x dx (very important)
1:08:12 – Question 12 - integral tan^-1 x dx (very important)
1:11:22 – Question 07 - integral x sec^-1 x dx (very important)
1:16:02 – Question 04 - integral x^2 lnx dx
1:17:56 – Question 05 - integral y sin2y dy
1:20:18 – Question 09 - integral x^2 e^x dx
1:24:09 – Extra- integral x^3 e^x dx
1:26:51 – Question 16 - integral x^3 e^(x^2) dx (important)
1:31:22 – Question 13 - integral x sec^2x dx (important)
1:34:12 – Question 14 - integral x sin^-1x dx (very very Important)
1:44:15 – Question 06 - integral e^x cosx dx (very Important)
1:47:25 – Example - integral square root (a^2-x^2) dx (very Important)

🔥 Key Learning Outcomes:
✔ Understand the logic of Integration by Parts
✔ Apply ILATE rule to correctly choose 1st and second
✔ Solve all types of complex integrals with confidence
✔ Prepare fully for board exams using Federal Board Class 12 Math New Book
✔ Master Exercise 3.4 with in-depth understanding and smart techniques

Keywords
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📎 Hashtags


📌 Let’s make math easy and enjoyable – together!

📚 F.Sc Part 2 || 12th Class Mathematics || Federal Board New Book 2025– Integration by Parts in Urdu/Hindi

Exercise 3.4 Class 12 Maths || Federal Board New Book 2025 || integration by Parts || by Dr Rizwan PDF Notes of this Lecture 👉 https://drive.google.com/drive/folders/1f0GBAYVIozPJvJWkX6mjaPkyzLzdL_gN?usp=sharingAssalamualaikum dear students! 👋Agar aap F...

Exercise 3.3 class 12 Math || Federal Board New Book 2025 || Integration by Substitution Method

https://youtu.be/sO7oimWVvSI

Assalamualaikum dear students! 👋
Agar aap 12th Class Mathematics (Federal Board) ke National Book Foundation ke Chapter 3: Integration ka next topic — Exercise 3.3 (Integration by Substitution) — asaani se seekhna chahte hain, toh yeh lecture aap ke liye hai ✅

Is video mein hum Integration by Substitution ko basic level se advance level tak samjhayenge — jisme U-substitution (basic variable substitution) aur trigonometric substitution techniques dono cover kiye jaayenge. Har question ki step-by-step solution ke saath aapko woh logic bhi samjhayenge jo aapko kisi bhi integration question ko solve karne ke liye chahiye hota hai.

📌 Topics Covered in This Lecture:
🔹 Basic idea behind substitution method (U-substitution)
🔹 When and how to choose the substitution variable (u = f(x))
🔹 Trigonometric substitution for functions like √(a² − x²), √(x² + a²), √(x² − a²)
🔹 Derivatives and substitution – how they help in integration
🔹 How to reverse substitution and finalize your integral
🔹 Complete solutions of Exercise 3.3 (Federal Board New Book 2025)
🔹 Common mistakes students make and how to avoid them
🔹 Integration of rational and irrational functions using substitution
🔹 Tips to identify suitable substitutions instantly

🕒 Time Code (Exercise 3.3 Breakdown):
00:00 – Introduction and outline
02:19 – Concept of basic substitution (u-substitution)
05:48 – Trigonometric substitution introduction
Solving integrals involving √(a² − x²), √(x² + a²), √(x² − a²)
10:17 – Question 01 (very important)
16:01 – Question 05 (very important)
22:09 – Question 02 (very important)
26:26 – Question 06 (very important)
31:58 – Question 03
34:50 – Question 04
38:58 – Question 07 (important)
39:06 – Question 08
41:21 – Question 09
43:13 – Question 11
44:40 – Question 10 (important)
47:06 – Question 12 (important)
48:55– Extra Question 1--- integral e^tan^-1x/1+x^2 dx
50:04– Extra Question 2--- integral x e^(x^2) dx
51:06– Extra Question 3--- integral sin(e^y) e^y dy

🔥 Key Learning Outcomes:
✔ Understand the logic behind substitution
✔ Learn to apply u-substitution in polynomial and trigonometric functions
✔ Master trigonometric substitution in irrational expressions
✔ Gain confidence in solving complex integrals easily
✔ Be fully prepared for Exercise 3.3 in board exams

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🎓 Don’t forget to download the notes PDF from the link above and follow along in your book. Acha se samajhne ke liye har question ko video ke saath solve karte chalain.
Best of luck with your preparations! 💪📚

Exercise 3.3 || 12th Class Math || Federal Board New Book 2025 || National Book Foundation || Integration by Substitution (U-substitution + Trigonometric Substitution) || by Dr Rizwan

Exercise 3.3 class 12 Math || Federal Board New Book 2025 || Integration by Substitution Method PDF Notes of this Lecture 👉 https://drive.google.com/drive/folders/1f0GBAYVIozPJvJWkX6mjaPkyzLzdL_gN?usp=sharingExercise 3.3 || 12th Class Math || Federal ...

What's the Easiest Way to Find the Domain of a Function in Calculus?

https://youtu.be/RpW6r72wQho



📘 How to find the domain of a function?
This is how you can become an expert in this topic.

The domain of a function is the set of all possible input values (usually 'x' values) for which the function is defined and gives a real number as output.

👉 In simple words: it's what 'x' can be in the function.

For algebraic functions to give a real number output, ensure:

❌ There is no zero in the denominator (if any), and

❌ There is no negative number inside a square root (if any).

🔍 Example 1:
Function:
f(x) = 1 / (x - 2)

Tip:

Set denominator = 0
x - 2 = 0

Solve for x
x = 2

Remove this value from ℝ (the set of real numbers)

Domain:
ℝ – {2}
(All real numbers except 2)

🔍 Example 2:
Function:
f(x) = √(2 – x)

Tip:

Set the expression inside the root ≥ 0
2 – x ≥ 0

Solve the inequality for x
x ≤ 2

Domain:
(-∞, 2]

🎯 If you want more examples, check out the detailed video
https://youtu.be/r95ylanLRVo
where we explore
✅ Extensive Practice with Over 18 Questions Related to the Domain of Functions
1- f(x) = x^2-6
2- g(x) = x/x+3
3- h(x) = x+4/x^2-9
4- i(x) x/5x+2
5- j(x) = x/x^2+4
6- k(x) = sqrt(x+1)
7- f(x) = x+7
8- f(x) = 2x^2+1
9- f(x) = 2sqrt(x-5)
10- f(x) = |x-2|-1
11- f(x) = 1+sinx
12- f(x) = 3+\sqrt(x-2)
13- f(x) = 3e^x/7
14- f(x) = x^2-16/x+4
15- f(x) = (x-1)^2+1
16- f(x) = 1/x-1
17- f(x) = x-2/x+3
18- f(x) = x^2-x-6/x-3

Exercise 1.1 Class 12 Math Federal Board new book 2025 || National Science Foundation || by Dr Rizwan
📌 Let’s make math easy and enjoyable – together!

What's the Easiest Way to Find the Domain of a Function in Calculus? 📘 How to find the domain of a function?This is how you can become an expert in this t...

Exercise 3.4 Class 12 Maths || Federal Board New Book 2025 || integration by Parts || by Dr Rizwan
https://youtu.be/Ak2XhJ4GQ4Y?si=myypEqFkWHNovLPo

Assalamualaikum dear students! 👋
Agar aap FSc Part 2 Mathematics (Federal Board) ke National Book Foundation – Chapter 3: Integration ka Exercise 3.4 – Integration by Parts easily samajhna chahte hain, toh yeh video aap ke liye complete solution ke saath tayar ki gayi hai ✅

Integration by parts aik aisi technique hai jo 2 functions ke product ka integral nikaalne ke liye istemal hoti hai. Yeh asal mein product rule (jo hum differentiation mein use karte hain) ka ulta tareeqa hai. Is lecture mein hum Integration by Parts ka concept basic to advanced level tak explain karenge. Har question ka step-by-step solution, proper formula use, aur real exam tips share kiye gaye hain. Video Urdu mein hai taake har student asaani se seekh sake.

📌 Topics Covered in This Lecture:
🔹 What is Integration by Parts (with derivation)
🔹 Integration by Parts Formula: ∫1st2nd dx = 1st ·∫ 2nd dx− ∫[ ∫ 2nd dx . d/dx (1st) ] dx
🔹 How to choose 1st and 2nd (ILATE tip explained)
🔹 Solving integrals involving inverse trigonometric, logarithmic, algebraic, exponential & trigonometric functions
🔹 Solving complex integrals using repeated integration by parts
🔹 Full solution of Exercise 3.4 – Federal Board New Syllabus 2025
🔹 Most common mistakes in Integration by Parts
🔹 Extra tricky questions for practice (beyond textbook)
🔹 Best and easiest way to learn integration by parts

🕒 Time Code – Exercise 3.4 Breakdown
00:00 – Introduction and Overview
06:11 – What is Integration by Parts - Easy to learn formula
12:52 – How to choose first function and second function
17:38 – ILATE Tip – Choosing first and second function
25:45 – Question 01 - integral lnx dx
30:17 – Question 02 - integral (lnx)^2 dx
34:48 – Question 03 - integral sin(lnx) dx (very important)
42:11 – Question 08 - integral ln(2x+3) dx (very important)
47:30 – Question 18 - integral lnx/ under root(x) dx (very important)
51:49 – Question 15 - integral ln(x+under root(x^2+1) dx (very important)
1:00:09 – Question 11 - integral cos^-1 x dx (very important)
1:08:12 – Question 12 - integral tan^-1 x dx (very important)
1:11:22 – Question 07 - integral x sec^-1 x dx (very important)
1:16:02 – Question 04 - integral x^2 lnx dx
1:17:56 – Question 05 - integral y sin2y dy
1:20:18 – Question 09 - integral x^2 e^x dx
1:24:09 – Extra- integral x^3 e^x dx
1:26:51 – Question 16 - integral x^3 e^(x^2) dx (important)
1:31:22 – Question 13 - integral x sec^2x dx (important)
1:34:12 – Question 14 - integral x sin^-1x dx (very very Important)
1:44:15 – Question 06 - integral e^x cosx dx (very Important)
1:47:25 – Example - integral square root (a^2-x^2) dx (very Important)

🔥 Key Learning Outcomes:
✔ Understand the logic of Integration by Parts
✔ Apply ILATE rule to correctly choose 1st and second
✔ Solve all types of complex integrals with confidence
✔ Prepare fully for board exams using Federal Board Class 12 Math New Book
✔ Master Exercise 3.4 with in-depth understanding and smart techniques

Keywords
FSc part 2 math new book, Integration by Parts, Exercise 3.4 Integration, Federal Board New Book 2025, calculus integration class 12, integration rules 12th class, integration techniques for class 12, LIATE rule integration, integration of exponential functions, integration with logarithmic terms, Urdu math lecture class 12, math class 12 federal board, Dr Rizwan math lectures, integration in urdu for class 12, integral calculus chapter 3, national book foundation math 2025, solved questions integration by parts, repeated integration by parts, integration for FBISE 2025, urdu calculus lecture, math made easy in urdu, class 12 math in urdu, integration tricks 12th class

📎 Hashtags


📌 Let’s make math easy and enjoyable – together!

📚 F.Sc Part 2 || 12th Class Mathematics || Federal Board New Book 2025– Integration by Parts in Urdu/Hindi

Exercise 3.4 Class 12 Maths || Federal Board New Book 2025 || integration by Parts || by Dr Rizwan PDF Notes of this Lecture 👉 https://drive.google.com/drive/folders/1f0GBAYVIozPJvJWkX6mjaPkyzLzdL_gN?usp=sharingAssalamualaikum dear students! 👋Agar aap F...

TikTok · booma_exam preparation Check out booma_exam preparation’s video.

https://youtu.be/lA4iENsEVm8?si=fzCWs3sFBlUsmTVJ

11th Class Exercise 9.1 | Trigonometric Functions | NBF | booma NBF.1109.9100 Hello students,In this lecture, we will discuss Exercise 9.1 from the 11th Class Federal Board (FBISE) new curriculum by the National Book Foundation (NBF). ...