10.3 u Substitution Definite Integrals NOTES Evaluate the indefinite integrals using u substitution. Write your questions here! β« 1 β1 β 4π₯ 2 ππ₯ Evaluate the indefinite integrals using u substitution. β« π₯ βπ₯ + 1 ππ₯ DEFINITE INTEGRAL 2 β« π‘ 2 βπ‘ 3 + 1ππ‘ 0 INVERSE TRIG Evaluate the definite integrals using u substitution. π 2 β« cos(π₯)βsin(π₯) ππ₯ 0 π β« 0 SUMMARY: Now, summarize your notes here! π₯2 π₯ ππ₯ +4 10.3 u Substitution Definite Integrals Evaluate the definite integral. 1 1. β«0 π₯ (π₯ 2 +1)3 ππ₯ π 2. β«02 sin(2π₯) ππ₯ 3 3. β«0 2π₯β3π₯ β 5 ππ₯ 10 4. β«1 β5π₯ β 1 ππ₯ PRACTICE Evaluate the definite integral. 3 1 5. β«β2 1+9π‘ 2 ππ‘ 5 6. β«1 π₯β2π₯ β 1ππ₯ 6 7. β«3 (π₯ 2 β 2π₯)ππ₯ 3 8. β«1 8π₯ β1β16π₯ 2 ππ₯ Evaluate the definite integral. β π 4 9. β« π β 8 βπ₯csc 2 (2π₯ 2 ) ππ₯ cot(2π₯ 2 ) 1 π¦ 2 + 2π¦ 10. β« 3 ππ¦ 3 + 3π¦ 2 + 4 βπ¦ 0 10.3 u Substitution Definite Integrals MULTIPLE CHOICE TEST PREP l 3 14. An equivalent representation of the definite integral β«1 2 cos(π₯ 2 )ππ₯ is 3 (A) β«1 cos π’ ππ’ 9 (B) β«1 cos π’ ππ’ β3 (C) β«1 cos π’ ππ’ 9 (D) β«1 2βπ’ cos π’ ππ’ β3 (A) β«1 2βπ’ cos π’ ππ’ 5. B 12. C 9. C 13. E 14. B
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