Ex 7.8, 12 - Chapter 7 Class 12 Integrals

Last updated at April 16, 2024 by

Slide25.JPG

Slide26.JPG

Transcript

Ex 7.8, 12 ∫_0^(𝜋/2)▒〖𝑐𝑜𝑠2 𝑥 𝑑𝑥〗 Step 1 :- Let F(𝑥)=∫1▒〖𝑐𝑜𝑠^2 𝑥 𝑑𝑥〗 = ∫1▒(cos⁡2𝑥 + 1)/2 𝑑𝑥 =1/2 ∫1▒〖𝑐𝑜𝑠 2𝑥 𝑑𝑥+1/2 ∫1▒𝑑𝑥〗 =1/2 × (𝑠𝑖𝑛 2𝑥)/2+𝑥/2 =1/4 𝑠𝑖𝑛 2𝑥+ 𝑥/2 Hence , F(𝑥)=1/4 𝑠𝑖𝑛 2𝑥+ 𝑥/2 Step 2 :- ∫_0^(𝜋/2)▒〖𝑐𝑜𝑠^2 𝑥=𝐹(𝜋/2)−𝐹(0) 〗 =1/4 𝑠𝑖𝑛(2 ×𝜋/2)+((𝜋/2))/2−1/4 𝑠𝑖𝑛(2×0/2)−0/2 =1/4 𝑠𝑖𝑛(𝜋)+𝜋/4−1/4 〖 sin〗⁡〖0 −0〗 =1/4 ×0+ 𝜋/4− 1/4 ×0−0 = 𝝅/𝟒

Go Ad-free
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 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.