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Formulas For Integrals List Of Integrals For 7.2-7.8.pdf

- StudyBlue
- Mississippi
- Mississippi State University
- Calculus
- Calculus 1723
- Amber Robinson
- Formulas For Integrals List Of Integrals For 7.2-7.8.pdf

Turner A.

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What is coming up due? In some circumstances, our π’-substitution can be in the form of a trig equation. This is particularly true with square roots. Be sure to factor the denominator. It can be shown that any polynomial in the denominator can be factored as a product of linear factors (like ππ₯ + π) and irreducible quadratic factors (like ππ₯2 + ππ₯ + π, where π2 β 4ππ < 0). We will break these down by cases. Cases Partial Fraction Breakdown Case I: Denominator is a product of distinct linear factors π
(π₯) π(π₯) = π΄ π1π₯ + π1 + π΅ π2π₯ + π2 + πΆ π3π₯ + π3 + β― Case II: Denominator is product of linear factors, some of which are repeated π
(π₯) π(π₯) = π΄ π1π₯ + π1 + π΅ π1π₯ + π1 2 + πΆ π1π₯ + π1 3 + β― Case III: Denominator contains irreducible quadratic factors, none of which repeat π΄π₯ + π΅ ππ₯2 + ππ₯ + π Case IV: Denominator contains repeated irreducible quadratic factors π΄π₯ + π΅ ππ₯2 + ππ₯ + π + πΆπ₯ + π· ππ₯2 + ππ₯ + π 2 + πΈπ₯ + πΉ ππ₯2 + ππ₯ + π 3 + β― For future reference: A Comparison Test for Improper Integrals Sometimes it is impossible to find the exact value of an improper integral and yet it is important to know whether it is convergent or divergent. In such cases the following theorem is useful. Although we state it for Type 1 integrals, a similar theorem is true for Type 2 integrals. Derivatives of Inverse Trig Functions