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Ex 7.9, 3 - Direct Integrate (4x3 - 5x2 + 6x + 9) dx - Ex 7.9

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  1. Chapter 7 Class 12 Integrals
  2. Serial order wise
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Transcript

Ex7.9, 3 1﷮2﷮(4𝑥3−5𝑥2+6𝑥+9) 𝑑𝑥﷯ Step 1 :- F 𝑥﷯= ﷮﷮ 4 𝑥﷮3﷯−5 𝑥﷮2﷯+6𝑥+9﷯𝑑𝑥﷯ = 4 𝑥﷮3+1﷯﷮3+1﷯− 5 𝑥﷮2+1﷯﷮2+1﷯+ 6 𝑥﷮1+1﷯﷮1+1﷯+9𝑥 = 4 𝑥﷮4﷯﷮4﷯− 5 𝑥﷮3﷯﷮3﷯+ 6 𝑥﷮2﷯﷮2﷯+9𝑥 = 𝑥﷮4﷯− 5﷮3﷯ 𝑥﷮3﷯+ 3𝑥﷮2﷯+9𝑥 Hence f(x) =𝑥﷮4﷯− 3 𝑥﷮3﷯﷮3﷯+3 𝑥﷮2﷯+9𝑥 Step 2 :- 1﷮2﷮ 4 𝑥﷮2﷯−9 𝑥﷮2﷯+6𝑥+9﷯𝑑𝑥 ﷯ =𝐹 2﷯−𝐹 1﷯ = 2﷯﷮4﷯− 5﷮3﷯ 2﷯﷮3﷯+3 2﷯﷮2﷯+9 2﷯− 1﷮4﷯− 5﷮3﷯ × 1﷮3﷯+3 × 1﷮2﷯+9 ×1﷯ =16− 5﷮3﷯ ×8+3 ×4+9 ×2−1+ 5﷮3﷯−3−9 =16− 40﷮3﷯ +12+18−1+ 5﷮3﷯−3−9 =33− 35﷮3﷯ = 3 33﷯ − 35﷮3﷯ = 𝟔𝟒﷮𝟑﷯

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