(Solved): During the past week of class Kota and Tyler explain they heard some terms th ...

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During the past week of class Kota and Tyler explain they heard some terms they are to understand. In particular, they are struggling with what makes an integral improper and what it means for an improper integral to converge or diverge. In their textbook, they found the following problems in the section on improper integrals. $${?}_1^{?}\frac{e^{?\sqrt{x}}}{\sqrt{x}}dx$$ $${?}_{?1}^1\frac{e^x}{e^x?1}dx$$ (a) Explain to Kota and Tyler what makes each of these integrals improper. (b) Describe what it means for an improper integral to converge or diverge. To help illustrate your explanation, determine whether each integral converges or diverges. If the integral converges, find its value.