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Example 4 - Find anti derivative F of f(x) = 4x3 - 6, f(0) = 3 - Using Formulaes

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Example 4 Find the anti derivative F of f defined by 𝑓 𝑥﷯= 4𝑥﷮3﷯−6, Where F (0) = 3 𝑓 𝑥﷯=4 𝑥﷮3﷯−6 Some F is Anti derivative F 𝑥﷯= ﷮﷮𝑓 𝑥﷯𝑑𝑥﷯ = ﷮﷮ 4 𝑥﷮3﷯−6﷯𝑑𝑥﷯ = ﷮﷮4 𝑥﷮3﷯𝑑𝑥−6𝑑𝑥﷯ = ﷮﷮4 𝑥﷮3﷯𝑑𝑥﷯− ﷮﷮6𝑑𝑥﷯ =4 ﷮﷮ 𝑥﷮3﷯𝑑𝑥﷯−6 ﷮﷮1.𝑑𝑥﷯ =4 ﷮﷮ 𝑥﷮3﷯𝑑𝑥﷯−6 ﷮﷮ 𝑥﷮0﷯ 𝑑𝑥﷯ =4 ﷮﷮ 𝑥﷮3﷯𝑑𝑥﷯−6 ﷮﷮ 𝑥﷮0﷯ 𝑑𝑥﷯ = 4 . 𝑥﷮3 + 1﷯ ﷮3 + 1﷯﷯+𝐶1﷯− 6 𝑥﷮0 + 1﷯﷮0 + 1﷯﷯−𝐶2﷯ = 4 . 𝑥﷮4﷯ ﷮4﷯﷯+𝐶1﷯− 6 𝑥﷮1﷯﷮1﷯﷯−𝐶2﷯ = 𝑥﷮4﷯+𝐶1−6𝑥−𝐶2 = 𝑥﷮4﷯−6𝑥+ 𝐶1−𝐶2﷯ = 𝑥﷮4﷯−6𝑥+𝐶 So, F 𝑥﷯= 𝑥﷮4﷯+6𝑥+𝐶 Given F 0﷯=3 So, F 𝑥﷯= 𝑥﷮4﷯+6𝑥+𝐶 3=0+0+𝐶 C = 3 So, F 𝒙﷯= 𝒙﷮𝟒﷯+𝟔𝒙+𝟑

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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