Ex 7.9, 18 - Direct Integrate (sin2 x / 2 - cos2 x / 2) dx - Definate Integration - By Formulae

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  1. Chapter 7 Class 12 Integrals
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Ex7.9, 18 0﷮𝜋﷮ s𝑖𝑛﷮2﷯﷮ 𝑥﷮2﷯﷯− cos﷮2﷯﷮ 𝑥﷮2﷯﷯﷯﷯ 𝑑𝑥 Step 1 :- Let F 𝑥﷯= ﷮﷮ sin﷮2﷯﷮ 𝑥﷮2﷯− cos﷮2﷯﷮ 𝑥﷮2﷯﷯﷯﷯𝑑𝑥﷯ =− ﷮﷮ cos﷮2﷯﷮ 𝑥﷮2﷯− sin﷮2﷯﷮ 𝑥﷮2﷯﷯﷯﷯𝑑𝑥﷯ =− ﷮﷮ cos﷮𝑥﷯𝑑𝑥﷯ =− sin﷮𝑥﷯ Hence F 𝑥﷯=− sin﷮𝑥﷯ Step 2 :- 0﷮𝜋﷮ 𝑠𝑖 𝑛﷮2﷯ 𝜋﷮2﷯−𝑐𝑜 𝑠﷮2﷯ 𝑥﷮2﷯﷯﷯𝑑𝑥=𝐹 𝜋﷯−𝐹 0﷯ =− 𝑠𝑖𝑛 𝜋﷮+ 𝑠𝑖𝑛 0﷯﷯ =− 0+0 = 𝟎

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