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Example 4 - Chapter 7 Class 12 Integrals
Last updated at Dec. 16, 2024 by Teachoo
Examples
Example 1 (i)
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Chapter 7 Class 12 Integrals
Serial order wise
Transcript
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
