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Ex 7.8
Ex 7.8, 2
Ex 7.8, 3
Ex 7.8, 4 Important
Ex 7.8, 5
Ex 7.8, 6
Ex 7.8, 7
Ex 7.8, 8 Important
Ex 7.8, 9
Ex 7.8, 10
Ex 7.8, 11 Important
Ex 7.8, 12 You are here
Ex 7.8, 13
Ex 7.8, 14 Important
Ex 7.8, 15
Ex 7.8, 16 Important
Ex 7.8, 17 Important
Ex 7.8, 18
Ex 7.8, 19 Important
Ex 7.8, 20 Important
Ex 7.8, 21 (MCQ) Important
Ex 7.8, 22 (MCQ)
Last updated at June 13, 2023 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