Ex 7.8, 18 - Chapter 7 Class 12 Integrals

Last updated at Dec. 16, 2024 by Teachoo

Ex 7.8, 18 - Direct Integrate (sin2 x / 2 - cos2 x / 2) dx - Ex 7.8

part 2 - Ex 7.8, 18 - Ex 7.8 - Serial order wise - Chapter 7 Class 12 Integrals

Next: Misc 35 → Remove Ads

Transcript

Ex 7.8, 18 ∫_0^𝜋▒(〖s𝑖𝑛〗^2⁡〖𝑥/2〗−cos^2⁡〖𝑥/2〗 ) 𝑑𝑥 Step 1 :- Let F(𝑥)=∫1▒(sin^2⁡〖𝑥/2−cos^2⁡〖𝑥/2〗〗 )𝑑𝑥 =−∫1▒(cos^2⁡〖𝑥/2−sin^2⁡〖𝑥/2〗〗 )𝑑𝑥 =−∫1▒〖cos⁡𝑥 𝑑𝑥〗 =−sin⁡𝑥 Hence F(𝑥)=−sin⁡𝑥 Step 2 :- ∫_0^𝜋▒(𝑠𝑖𝑛^2 𝜋/2−𝑐𝑜𝑠^2 𝑥/2) 𝑑𝑥=𝐹(𝜋)−𝐹(0) =−〖𝑠𝑖𝑛 𝜋〗⁡〖+ 𝑠𝑖𝑛(0)〗 =− 0+0 = 𝟎

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo

Class 6

Class 7

Class 8

Class 9

Class 10

Class 11

Class 12

Courses

Interesting

Popular