Examples

Chapter 7 Class 12 Integrals
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### Transcript

Example 4 Find the anti derivative F of f defined by π(π₯)=γ4π₯γ^3β6, Where F (0) = 3 π(π₯)=4π₯^3β6 Some F is Anti derivative F(π₯)=β«1βπ(π₯)ππ₯ =β«1β(4π₯^3β6)ππ₯ =β«1βγ4π₯^3 ππ₯β6ππ₯γ =β«1βγ4π₯^3 ππ₯γββ«1β6ππ₯ =4β«1βγπ₯^3 ππ₯γβ6β«1βγ1.ππ₯γ =4β«1βγπ₯^3 ππ₯γβ6β«1βγπ₯^0 ππ₯γ =(4 . ((π₯^(3 + 1) )/(3 + 1))+πΆ1)β(6(π₯^(0 + 1)/(0 + 1))βπΆ2) =(4 . ((π₯^4 )/4)+πΆ1)β(6(π₯^1/1)βπΆ2) =π₯^4+πΆ1β6π₯βπΆ2 =π₯^4β6π₯+(πΆ1βπΆ2) =π₯^4β6π₯+πΆ So, F(π₯)=π₯^4β6π₯+πΆ Given F(0)=3 So, F(π₯)=π₯^4β6π₯+πΆ 3=0+0+πΆ" " "C = 3" So, F(π)=π^πβππ+π

#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.