Ex 7.9, 7 - Direct Integrate tan x dx from 0 to pi/4 - Ex 7.9

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Ex7.9, 7 0﷮ 𝜋﷮4﷯﷮ 𝑡𝑎𝑛 𝑥﷮𝑑𝑥﷯﷯ Step 1 :- F 𝑥﷯= ﷮﷮ tan﷮𝑥﷯ 𝑑𝑥﷯ =𝑙𝑜𝑔 𝑠𝑒𝑐 𝑥﷯ Hence F 𝑥﷯=𝑙𝑜𝑔 𝑠𝑒𝑐 𝑥﷯ Step 2 :- 0﷮ 𝜋﷮4﷯﷮ tan﷮𝑥 𝑑𝑥=𝐹 𝜋﷮4﷯﷯−𝐹 0﷯﷯﷯ =𝑙𝑜𝑔 𝑠𝑒𝑐 𝜋﷮4﷯﷯﷯−𝑙𝑜𝑔 𝑠𝑒𝑐 0﷯﷯ =𝑙𝑜𝑔 ﷮2﷯﷯−𝑙𝑜𝑔 1﷯ = log﷮ ﷮2﷯﷯−0 = log﷮ ﷮2﷯﷯ = log﷮ 2﷮ 1﷮2﷯﷯﷯ = 𝟏﷮𝟐﷯ 𝒍𝒐𝒈﷮𝟐﷯

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