Chapter 7 Class 12 Integrals
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Example 4 - Chapter 7 Class 12 Integrals

Last updated at July 28, 2026 by

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

Example 4 - Chapter 7 Class 12 Integrals - Part 2

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Example 4 Find the anti derivative F of f defined by š‘“(š‘„)=怖4š‘„怗^3āˆ’6, Where F (0) = 3 š‘“(š‘„)=4š‘„^3āˆ’6 Some F is Anti derivative F(š‘„)=āˆ«1ā–’š‘“(š‘„)š‘‘š‘„ =āˆ«1ā–’(4š‘„^3āˆ’6)š‘‘š‘„ =āˆ«1ā–’怖4š‘„^3 š‘‘š‘„āˆ’6š‘‘š‘„怗 =āˆ«1ā–’怖4š‘„^3 š‘‘š‘„怗āˆ’āˆ«1ā–’6š‘‘š‘„ =4āˆ«1ā–’怖š‘„^3 š‘‘š‘„怗āˆ’6āˆ«1ā–’怖1.š‘‘š‘„怗 =4āˆ«1ā–’怖š‘„^3 š‘‘š‘„怗āˆ’6āˆ«1ā–’怖š‘„^0 š‘‘š‘„怗 =(4 . ((š‘„^(3 + 1) )/(3 + 1))+š¶1)āˆ’(6(š‘„^(0 + 1)/(0 + 1))āˆ’š¶2) =(4 . ((š‘„^4 )/4)+š¶1)āˆ’(6(š‘„^1/1)āˆ’š¶2) =š‘„^4+š¶1āˆ’6š‘„āˆ’š¶2 =š‘„^4āˆ’6š‘„+(š¶1āˆ’š¶2) =š‘„^4āˆ’6š‘„+š¶ So, F(š‘„)=š‘„^4āˆ’6š‘„+š¶ Given F(0)=3 So, F(š‘„)=š‘„^4āˆ’6š‘„+š¶ 3=0+0+š¶" " "C = 3" So, F(š’™)=š’™^šŸ’āˆ’šŸ”š’™+šŸ‘

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