Ex 7.8, 12 - Chapter 7 Class 12 Integrals
Last updated at April 16, 2024 by Teachoo
Definite Integration - By Formulae
Example 27 (i)
Ex 7.8, 3
Ex 7.8, 6
Ex 7.8, 2
Misc 28
Ex 7.8, 4 Important
Ex 7.8, 5
Ex 7.8, 7
Ex 7.8, 8 Important
Ex 7.8, 17 Important
Ex 7.8, 12 You are here
Ex 7.8, 18
Misc 35
Misc 36 Important
Ex 7.9, 2 Important
Ex 7.8, 20 Important
Ex 7.8, 9
Ex 7.8, 10
Ex 7.8, 21 (MCQ) Important
Ex 7.8, 22 (MCQ)
Ex 7.8, 14 Important
Ex 7.8, 19 Important
Ex 7.9, 10 (MCQ) Important
Ex 7.9, 8
Misc 33
Misc 37
Ex 7.9, 3 Important
Definite Integration - By Formulae
Last updated at April 16, 2024 by Teachoo
Ex 7.8, 12 ∫_0^(𝜋/2)▒〖𝑐𝑜𝑠2 𝑥 𝑑𝑥〗 Step 1 :- Let F(𝑥)=∫1▒〖𝑐𝑜𝑠^2 𝑥 𝑑𝑥〗 = ∫1▒(cos2𝑥 + 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