MAT136H1 Lecture Notes - Improper Integral, Trigonometric Functions
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MAT136H1 Full Course Notes
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Question #2 (easy): improper integral with infinite discontinuity. Whether the improper integral converges or diverges, they are still considered improper integrals and grouped under type 1 (infinite interval) and type 2 (finite interval, but infinite discontinuity due to vertical asymptotes caught within the finite interval). Notice that the interval is fixed over real numbers [ ]. However, examining the functions in the integral, one is a reciprocal trigonometric function and the other a fractional trigonometric function, where and. Since periodically takes on the value of , there are cyclical vertical asymptotes where , which means whenever lies within the interval [ ], there is an infinite discontinuity. where k is any integer.
