MAT136H1 Lecture 9: 7.7 Comparing Improper Integrals
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77comparingimproperintldf. in ding an exact value of an improper integral is often hard so we can often apure it with aknownintegral tosay ifgiven integel converges diverges. Sometimes it"shard to findthe exactvalueof an mpoperintybyan. lidifferentiation but it maybe possible todeterminewhether anmgmtcoverages or diverges. Say gcxsfyfgs. de converges glxsfx. fgx. dk diverges uhenpsl. ff. ch if fistvelcontmousonia. bg. Converges when psi converges when pei gg e ax dxonvergesuhe. ua 0 diverges diverges uhenp 1 diverges when a 0 g gadx 3ft dx and g fcxdx_diverges if dx also converges. Fix a c is polynomial depends on integral is always continuous convergeslarge. Compare with f e dx which converges if tndx also converges week. Dx dxg. orgthe that qs assigned to reviewlast. Converges i it converges h x w. If y is positive and continuous on a then and ffdx either both. At a constant t. ifc lyy. ie yjf t particularsolution. Check f 1 x4112 is solution or m y 1 when 0 is a solution fix 1 hotalways unique solution to am iup.
