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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 𝑓(π‘₯)=γ€–4π‘₯γ€—^3βˆ’6, Where F (0) = 3 𝑓(π‘₯)=4π‘₯^3βˆ’6 Some F is Anti derivative F(π‘₯)=∫1▒𝑓(π‘₯)𝑑π‘₯ =∫1β–’(4π‘₯^3βˆ’6)𝑑π‘₯ =∫1β–’γ€–4π‘₯^3 𝑑π‘₯βˆ’6𝑑π‘₯γ€— =∫1β–’γ€–4π‘₯^3 𝑑π‘₯γ€—βˆ’βˆ«1β–’6𝑑π‘₯ =4∫1β–’γ€–π‘₯^3 𝑑π‘₯γ€—βˆ’6∫1β–’γ€–1.𝑑π‘₯γ€— =4∫1β–’γ€–π‘₯^3 𝑑π‘₯γ€—βˆ’6∫1β–’γ€–π‘₯^0 𝑑π‘₯γ€— =(4 . ((π‘₯^(3 + 1) )/(3 + 1))+𝐢1)βˆ’(6(π‘₯^(0 + 1)/(0 + 1))βˆ’πΆ2) =(4 . ((π‘₯^4 )/4)+𝐢1)βˆ’(6(π‘₯^1/1)βˆ’πΆ2) =π‘₯^4+𝐢1βˆ’6π‘₯βˆ’πΆ2 =π‘₯^4βˆ’6π‘₯+(𝐢1βˆ’πΆ2) =π‘₯^4βˆ’6π‘₯+𝐢 So, F(π‘₯)=π‘₯^4βˆ’6π‘₯+𝐢 Given F(0)=3 So, F(π‘₯)=π‘₯^4βˆ’6π‘₯+𝐢 3=0+0+𝐢" " "C = 3" So, F(𝒙)=𝒙^πŸ’βˆ’πŸ”π’™+πŸ‘

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.