Chapter 7 Class 12 Integrals
Concept wise

Example 4 - Chapter 7 Class 12 Integrals

Last updated at Dec. 16, 2024 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 𝑓(𝑥)=〖4𝑥〗^3−6, Where F (0) = 3 𝑓(𝑥)=4𝑥^3−6 Some F is Anti derivative F(𝑥)=∫1▒𝑓(𝑥)𝑑𝑥 =∫1▒(4𝑥^3−6)𝑑𝑥 =∫1▒〖4𝑥^3 𝑑𝑥−6𝑑𝑥〗 =∫1▒〖4𝑥^3 𝑑𝑥〗−∫1▒6𝑑𝑥 =4∫1▒〖𝑥^3 𝑑𝑥〗−6∫1▒〖1.𝑑𝑥〗 =4∫1▒〖𝑥^3 𝑑𝑥〗−6∫1▒〖𝑥^0 𝑑𝑥〗 =(4 . ((𝑥^(3 + 1) )/(3 + 1))+𝐶1)−(6(𝑥^(0 + 1)/(0 + 1))−𝐶2) =(4 . ((𝑥^4 )/4)+𝐶1)−(6(𝑥^1/1)−𝐶2) =𝑥^4+𝐶1−6𝑥−𝐶2 =𝑥^4−6𝑥+(𝐶1−𝐶2) =𝑥^4−6𝑥+𝐶 So, F(𝑥)=𝑥^4−6𝑥+𝐶 Given F(0)=3 So, F(𝑥)=𝑥^4−6𝑥+𝐶 3=0+0+𝐶" " "C = 3" So, F(𝒙)=𝒙^𝟒−𝟔𝒙+𝟑

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo