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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


Transcript

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 is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.