Chapter 7 Class 12 Integrals
Concept wise

Ex 7.3, 1 - Chapter 7 Class 12 Integrals

Last updated at Feb. 25, 2025 by

Ex 7.3, 1 Class 12 Maths - NCERT Solution - Integrate sin^2 (2x + 5) - Ex 7.3

part 2 - Ex 7.3, 1 - Ex 7.3 - Serial order wise - Chapter 7 Class 12 Integrals

Remove Ads

Transcript

Ex 7.3, 1 Find the integral of sin2 (2π‘₯ + 5) ∫1β–’γ€–π’”π’Šπ’πŸ (πŸπ’™ + πŸ“) γ€— 𝒅𝒙 =∫1β–’(1 βˆ’ γ€–π‘π‘œπ‘  2〗⁑(2π‘₯ + 5))/2 𝑑π‘₯ =1/2 ∫1β–’γ€–1βˆ’cos⁑(4π‘₯+10) γ€— 𝑑π‘₯ =1/2 [∫1β–’1 𝑑π‘₯βˆ’βˆ«1β–’cos⁑(4π‘₯+10) 𝑑π‘₯] We know that 𝐜𝐨𝐬 𝟐𝜽=πŸβˆ’πŸ γ€–π’”π’Šπ’γ€—^𝟐⁑𝜽 2 sin^2 πœƒ=1βˆ’cos⁑2πœƒ sin^2 πœƒ=1/2 [1βˆ’cos⁑2πœƒ ] Replace πœƒ by (𝟐𝐱+πŸ“) sin^2 (2π‘₯+5)=(1 βˆ’ cos⁑2(2π‘₯ + 5))/2 As ∫1β–’cos⁑(π‘Žπ‘₯+𝑏) 𝑑π‘₯=sin⁑(π‘Žπ‘₯ + 𝑏)/π‘Ž+𝐢 =1/2 [π‘₯βˆ’ sin⁑(4π‘₯ + 10)/4 +𝐢] =𝒙/𝟐 βˆ’ 𝟏/πŸ– π’”π’Šπ’β‘(πŸ’π’™+𝟏𝟎)+π‘ͺ

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 15 years. He provides courses for Maths, Science and Computer Science at Teachoo