Ex 7.8, 18 - Chapter 7 Class 12 Integrals

Last updated at April 16, 2024 by Teachoo

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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

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