Class 12 Maths Integrals Chapter 7 Part 2 🔥 Important Trigonometric Integrals | NCERT | Faiz Sir

Is video me Class 12 Maths – Chapter 7 (Integrals) Part 2 ko detail me explain kiya gaya hai.
Yeh lecture NCERT based hai aur board exams + competitive exams ke liye bahut important hai.

📌 Is lecture me aap seekhenge:
✔ Some Important Integrals involving Trigonometric Functions
✔ ∫tan x dx, ∫cot x dx, ∫sec x dx, ∫cosec x dx ke short tricks & proofs
✔ Mixed type NCERT Examples step-by-step
✔ Exercise based important integrals (1–9)
✔ Objective MCQs (Choose the correct answer) jo exams me direct aate hain

📘 Covered Topics:
🔹 Trigonometric Integrals
🔹 Substitution method
🔹 Standard integrals
🔹 NCERT Exercise questions
🔹 Board exam oriented practice

👨‍🏫 By: Faiz Sir (M.Sc. Maths with CS)
📚 Class: 12
📖 Chapter: 7 – Integrals
🏫 Board: CBSE | NCERT

👉 Agar aap Class 12 Maths Integrals ko easily samajhna chahte hain, to yeh video must watch hai.
👍 Video ko Like, Share & Subscribe zaroor karein – Infinix Classes Maths by Faiz Sir



#class12maths
#integrals
#Chapter7Integrals
#trigonometricintegrals
#ncertmaths
#cbseclass12
#boardexam2026
#mathsbyfaizsir
#infinixclasses
#integralcalculus
#Class12BoardMaths
#ImportantIntegrals
#mathstricks
#ncertsolutions



class 12 maths integrals, chapter 7 integrals class 12, integrals ncert class 12, trigonometric integrals, important integrals class 12, integrals by faiz sir, infinix classes maths, cbse class 12 maths, board exam maths class 12, integration tricks, calculus class 12, definite and indefinite integrals, ncert integrals solutions, maths class 12 chapter 7, integrals examples, trigonometric integration, maths in hindi, class 12 maths hindi medium, integrals part 2


INTEGRALS | Class - 12 | Chapter – 7 | NCERT By : FAIZ SIR


Some Important Integrals Involving Trigonometric Functions:
(i) ∫tan x dx = log |sec x| + C
(ii) ∫cot x dx = log |sin x| + C
(iii) ∫sec x dx = log |sec x + tan x| + C
(iv) ∫cosec x dx = log |cosec x – cot x| + C


Example : Find the following integrals:
(i) ∫sin3x cos2x dx (ii) ∫𝐬𝐢𝐧⁡𝒙/𝐬𝐢𝐧⁡〖(𝒙 + 𝒂)〗 dx (iii) ∫𝟏/(𝟏 + 𝐭𝐚𝐧⁡𝒙 ) dx


Integrate the functions in Exercises 1 to 9:
1. 𝟐𝒙/(𝟏+ 𝒙^𝟐 ) 2. 𝟏/(𝒙 + 𝒙 𝒍𝒐𝒈 𝒙)

3. sin (ax + b) cos (ax + b)

4. (𝒙^𝟑 −𝟏)^(𝟏/𝟑) 𝒙^𝟓

5. 𝟏/(𝒙 〖(𝒍𝒐𝒈 𝒙)〗^𝒎 ), 𝒙 is greater than 𝟎, 𝒎≠𝟏

6. 𝒆^〖𝒕𝒂𝒏〗^(−𝟏)⁡𝒙 /(𝟏+ 𝒙^𝟐 )

7. (𝟐 𝒄𝒐𝒔 𝒙 − 𝟑 𝒔𝒊𝒏 𝒙)/(𝟔 𝒄𝒐𝒔 𝒙 + 𝟒 𝒔𝒊𝒏 𝒙)


8. cot x log sin x

9. (𝒙^𝟑 𝒔𝒊𝒏 〖(𝒕𝒂𝒏〗^(−𝟏) 𝒙^𝟒))/(𝟏+ 𝒙^𝟖 )

Choose the correct answer in Exercises 1 and 2.
1. ∫ (𝟏𝟎 𝒙^𝟗+ 〖𝟏𝟎〗^𝒙 〖𝒍𝒐𝒈〗_𝒆 𝟏𝟎)/(𝒙^𝟏𝟎+ 〖𝟏𝟎〗^𝒙 ) dx equals
(A) 10x – x10 + C (B) 10x + x10 + C
(C) (10x – x10)-1 + C (D) log(10x + x10) + C

2. ∫ 𝒅𝒙/(〖𝒔𝒊𝒏〗^𝟐 𝒙〖 𝒄𝒐𝒔〗^𝟐 𝒙) equals
(A) tan x + cot x + C (B) tan x - cot x + C
(C) tan x cot x + C (D) tan x - cot 2x + C