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Example 4 - Chapter 7 Class 12 Integrals (Term 2)
Last updated at March 16, 2023 by Teachoo
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Chapter 7 Class 12 Integrals
Serial order wise
Transcript
Example 4 Find the anti derivative F of f defined by π(π₯)=γ4π₯γ^3β6, Where F (0) = 3 π(π₯)=4π₯^3β6 Some F is Anti derivative F(π₯)=β«1βπ(π₯)ππ₯ =β«1β(4π₯^3β6)ππ₯ =β«1βγ4π₯^3 ππ₯β6ππ₯γ =β«1βγ4π₯^3 ππ₯γββ«1β6ππ₯ =4β«1βγπ₯^3 ππ₯γβ6β«1βγ1.ππ₯γ =4β«1βγπ₯^3 ππ₯γβ6β«1βγπ₯^0 ππ₯γ =(4 . ((π₯^(3 + 1) )/(3 + 1))+πΆ1)β(6(π₯^(0 + 1)/(0 + 1))βπΆ2) =(4 . ((π₯^4 )/4)+πΆ1)β(6(π₯^1/1)βπΆ2) =π₯^4+πΆ1β6π₯βπΆ2 =π₯^4β6π₯+(πΆ1βπΆ2) =π₯^4β6π₯+πΆ So, F(π₯)=π₯^4β6π₯+πΆ Given F(0)=3 So, F(π₯)=π₯^4β6π₯+πΆ 3=0+0+πΆ" " "C = 3" So, F(π)=π^πβππ+π
