Ex 7.9, 17 - Direct Integrate (2 sec2 x + x3 + 2) dx - Ex 7.9

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Ex7.9, 17 0﷮ 𝜋﷮4﷯﷮ 2 sec﷮2﷯﷮𝑥﷯+ 𝑥﷮3﷯+2﷯﷯ 𝑑𝑥 Step 1 :- Let F 𝑥﷯= ﷮﷮ 2 sec﷮2﷯﷮𝑥+ 𝑥﷮3﷯+2﷯﷯ 𝑑𝑥﷯ =2 ﷮﷮ sec﷮2﷯﷮𝑥 𝑑𝑥﷯+ ﷮﷮ 𝑥﷮3﷯ 𝑑𝑥+ ﷮﷮2 𝑑𝑥﷯﷯﷯ =2 tan﷮𝑥+ 𝑥﷮4﷯﷮4﷯+2𝑥﷯ Hence F 𝑥﷯=2 tan﷮𝑥+ 𝑥﷮4﷯﷮4﷯+2𝑥﷯ Step 2 :- 0﷮ 𝜋﷮4﷯﷮ 2𝑠𝑒 𝑐﷮2﷯𝑥+ 𝑥﷮3﷯+2﷯𝑑𝑥=𝐹 𝜋﷮4﷯﷯−𝐹 0﷯﷯ = 2𝑡𝑎𝑛 𝜋﷮4﷯+ 𝜋﷮4﷯﷯﷮4﷯﷮4﷯+2 𝜋﷮4﷯﷯− 2𝑡𝑎𝑛 0﷯+ 0﷯﷮4﷯﷮4﷯+2 ×0﷯ =2𝑡𝑎𝑛 𝜋﷮4﷯+ 𝜋﷮4﷯﷮ 4﷮4﷯﷯ × 1﷮4﷯+ 𝜋﷮2﷯− 2×0+0+0﷯ =2 ×1+ 𝜋﷮4﷯﷮ 4﷮5﷯﷯+ 𝜋﷮2﷯−0 =𝟐+ 𝝅﷮𝟒﷯﷮𝟏𝟎𝟐𝟒﷯+ 𝝅﷮𝟐﷯

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