MATH 1004 Lecture Notes - Lecture 16: Opata Language, Improper Integral

• School: Carleton University
• Department: Mathematics
• Course: MATH 1004
• Professor: Glenn Mc Rae

Document Summary

7. 8 improper integrals: in same cases a de nite integral may have one or both of its limits in nite, this integral is an example of an improper integral. Such integrals can be grouped into two basics classes: those with one or both limits being in nite, those with both limits being nite, but the integrand being in nite somewhere inside the interval of integration. Case one: improper integral with in nite limit(s). (cid:90) a (cid:90) t a (cid:90) a f (x)dx = lim. Examples: determine the value of p for which the improper integral (cid:90) (cid:90) . 1 xp dx x2e xdx, converges or diverges: evaluate (cid:90) xe xdx, Case two: improper integral with an in nite discontinuity. Let f has discontinuous over [a, b) and assume that f has an in nite discontinuity at x=b. We de ne the improper integral of f over [a, b) by (cid:90) b a (cid:90) t a f (x)dx = lim.