MATH 1132Q Lecture 6: MATH 1132Q , Lecture 6 , Section 7.8 - Improper Integrals
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Math 1132q , lecture 6 , section 7. 8 - improper integrals. Improper integral - an integral that has an infinite bound, or an integral whose integrand has a discontinuity in the interval of integration. 0 1 / x dx discontinuity at x = 0. 0 tanx dx discontinuity at x = / 2. If the value of the improper integral exists, we say it converges, otherwise it diverges. [ lim (x - ) e^x = lim (x ) e^-x ] e^-2 - ( lim (x - ) e^x ) Take limit as x approaches improper boundary e^-2 - lim (x ) 1 / e^x. = e^-2 - 0 if the limits exist , the integral converges. 0 x ln x dx improper bound , ln x is undefined at x = 0. [ x^2 lnx - x ] [ x^2 lnx - x^2 ]
