Check sibling questions

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

Solve all your doubts with Teachoo Black (new monthly pack available now!)


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‘

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.