Integration Class 12 | JEE Main & Advanced

--------------
Master the art of Integration with this comprehensive session for Class 12 students, tailored for JEE Main & Advanced. 🧮 Dive deep into concepts of Integration. Learn the tricks to identify the method which needs to be applied in the given integration. Whether you're building your fundamentals or looking for a last-minute revision, this session will help you solve even the trickiest integration problems with ease. Perfect for boosting your calculus skills and scoring higher in your JEE exams!
--------------
--------------
#JEE #JEEMain #JEEmain2025 #JEEAdvanced #JEEAdvanced2025 #JEE2025 #JEEPreparation #ArvindKaliaSir #ArvindKaliaMaths #IITPreparation #Unacademy #JEENexus #Class12maths #IntegrationClass12 #Integration
--------------
TIMESTAMPS
0:00 Introduction & Nature of Chapter
6:08 Index and critical topics
9:01 Introduction & Some Standard Integrals
35:49 Integration by substitution
1:37:00 Integration of Algebraic formats
2:38:59 Integration by partial fractions
3:00:06 Integration by parts
3:54:16 Integration of trigonometric formats

[AkulAttre]

3:30:57 Question Done and dusted as well the partial fraction one which is at 2:52:13
Thanks a lot Sir for bringing this wonderful session.

[XNOSAMA]

1:12:21 - 1:12:49 : Revise after test.

1:40:09 - end: remaining

[v_rlegends]

Before this nothing was going well but after this chapter, started doing well and practicing more.
Thanks to you bhai ❤️

[einsteinium]

THANKS ALOT SIR!!! I am OVERWHELMED by the way you teach ALL the concepts including ADV. LEVEL with such an ease, it directly goes in head! Literally I feel you are one of THE BEST MATHEMATICS TEACHERS in INDIA. MERA BHAI MERA BHAI 🔥. You made it easy for me to enjoy learning.

[MohammadShahnawazFaiyaz-zz]

37:27 sir I never made that mistake and I sir when you're going to teach Differential Equations and your lecture are really very amazing and easy to understand thanks a lot ☺️☺️

[shaiksayyedbi]

TIMESTAMPS
0:00 Introduction & Nature of Chapter
6:08 Index and critical topics
9:01 Introduction & Some Standard Integrals
35:49 Integration by substitution
1:37:00 Integration of Algebraic formats
2:38:59 Integration by partial fractions
3:00:06 Integration by parts
3:54:16 Integration of trigonometric formats

[RajaHaris-qfhw]

Dear sir i am in 2nd year university but still listening your lectures to build up my knowledge and concepts

[cricke]

Hw done partial fraction wala aur bahut maja aya concept clr but (x^4+1)^2 me time laga par finally ho gya❤❤ # mera bhai

[BillionEditz]

This man is the best teacher you can ever see with lots of easy tricks ❤️❤️❤️

[me]

x⁴+1 ka square vala saval
Done and dusted

[target__iit]

𝐓𝐈𝐌𝐄𝐒𝐓𝐀𝐌𝐏𝐒 🚬(⁠´⁠ε⁠｀⁠ )
2:17 Nature of Chapter
5:37 Weightage
6:08 *Index*
7:19 Critical Topics

9:01 *Introduction*
9:54 *Some Standard Integrals*
11:15 *Other Formulas of ∫ (sec x) & ∫ (cosec x)*
13:56 *Basics of Integration*
14:27 Our aim in this chapter🔥
15:47 Questions involving Trigonometry
19:35 _🚬 Make denominator a single expression_
20:38 _🚬 Splitting Addition/Substraction_
22:32 _🚬 Complex Expression in Denominator makes us Unhappy_
23:54 _🚬 It’s prefer to keep angle same_
25:41 Questions involving Algebra
27:20 _🚬 –1+1 Manipulation_

36:07 *Integration by Substitution*
36:15 *Remark ⭐ { ∫ f(ax+b) dx if ∫ f(x) dx = F(x) }*
39:15 _Recall 🎩_
40:50 _🚬 (a+b)/c better than a/(b+c)_
43:59 _🚬 Spot the derivative in the expression_
47:06 _🚬 When log present & no idea comes in mind to solve it, then substitute it_
50:31 *NOTE 🚬* (Substitute x+√(x²+1) = t whenever you see them)
57:31 *NOTE ⭐* (Whenever a big power is inside another power, take common)
1:03:19 NOTE
1:08:19 ∫ 1/(ax+b)ᵐ (px+q)ⁿ dx
1:09:12 _🚬 Linear/Linear is Good, convert (Linear)(Linear) in denominator to it_
1:16:33 _🚬 If there's expression under √, ∛ etc in the Denominator, substitute it to make it a single term_
1:23:32 *Some Standard Substitutions*

1:26:31 *Integrals for Special Functions*
1:28:37 *NOTE*
1:33:40 _🚬 If you see a single or many eᵃˣ terms in the integrand, substitute it_

1:36:59 *Integration of Algebraic Expressions*
1:38:13 *Format 1️⃣:* L/Q or L/√Q̅
➙ L = Constant or Linear
1:48:43 _🚬 Speed Solving_
1:50:20 *Observations:*
1:50:23 ① ∫ f’(x)/f(x) dx
1:50:35 ② ∫ fⁿ(x)·f’(x) dx
1:50:48 ③ ∫ f’(x)/√{f(x)} dx

1:52:52 *Format 2️⃣:* Q/√Q̅
1:57:17 *Format 3️⃣:* P(x)/Q ➙ deg{P(x)} ≥ 2
2:03:45 *Format 4️⃣:* ∫ (x²±1)/(x⁴+Kx²+1) dx
Even powers of x
2:04:17 Remember this before
2:10:46 *Variations ✨*

2:21:00 *Format 5️⃣:* Linear or Quad with Linear or Quad under Sq Root in Denominator
2:30:50 *Variations*

2:32:19 *Examples to see dedicated use of Standard Substitution*

2:38:59 *Integration by Partial Fractions*
2:40:22 Formats (Only Proper Fractions)
2:48:38 *NOTE 🚬:* If all the terms are Pure Quadratic
2:50:49 *Thug Advise 🚬*: When to use Partial Fraction

3:00:06 *Integration by Parts*
3:02:30 Using by parts to integrate Logarithmic and Inverse functions
3:05:41 Recurring By Parts
3:07:48 Remember
3:10:04 _🚬 Higher Powers that can’t be handled_
3:12:04 _🚬Try to create I while solving by parts_
3:13:41 *NOTE STRATEGY🚬:* When there is big powers with Trigo in Denominator

3:20:34 *Forced By Parts ⚡*
3:32:20 *Two Classic Integrals*
3:34:36 _🚬 Try to create f + f’ yourself_
3:35:48 *⚡ Method to create f + f’*
3:37:44 _🚬 Don't deviate from the method, don't worry if something comes as product_
3:40:47 *General Version of ∫ eˣ·{f(x)+f’(x)} dx*

3:54:16 *Integration of Trigonometric Format*
3:54:47 *Format 1️⃣:* ∫ sinᵐx cosⁿx dx
∫ tanᵐx secⁿx dx
3:57:49 _If both m & n are even_
4:02:26 _If m and n are fractions_
4:06:14 *Format 2️⃣:* Linear in Sin & Cos in Denominator
4:09:22 _🚬 Clubbing Sin & Cos expression together_
4:10:44 *Format 3️⃣:* L/L ➙ Linear in Sin & Cos
4:12:37 *Format 4️⃣:* Even powers of Sin & Cos in Denominator

4:14:56 *THANK YOU*

[WAQUARANJUM-hg]

1:46:50 Answer is 1/2 ln|cosx-3/cosx-1|+C

[sanjaykumarsingh]

Awesome video on indefinite integration
Full on concept clear

[football]

Very important chapter and very quality lecture ❤
Done and dusted
Thankyou bhaii

[deepikatalwar]

SIR (X^4+1)^2 WALA QUESTION, DONE AND DUSTED IN 1 GO. PROCEDED LIKE PARTIAL FRACTION OF PURE QUADRATIC AFTER YOUR HINT

[AinyZahera]

Best math teacher on YouTube
❤❤❤❤❤❤❤❤❤
Mera bhai❤

[huuenmm]

3rd hours vale 35:00, 36:02, 38:05, 41:00, 48:00, 54 iske baad end tak sab he main hai kyuki jada question nhi the formats he the main main!!

[YashGarg-ns]

3:20:10 That's why you are a legendary Teacher sir❤❤

[prathmeshhambire]

1:44:20 yaha pe mistake ho gayi sir ji aap se... x ke coefficients compare karenge toh 4=2(lambda) ayega and the 2nd equation will be 1=3(lambda)+u

[shrirajdhore]

SIR DEFINITE INTEGRALS KA SESSION KAB RAHEGA?