Evaluate : ∫0∞xe-x⋅dx - Mathematics And Statistics

0Maharashtra State BoardHSC Science (General) 12th Standard Board ExamQuestion PapersQuestion Papers300Textbook Solutions13139MCQ Online Mock Tests73Important Solutions7574Concept Notes & Videos461Time Tables27SyllabusEvaluate: ∫0∞xe-x.dx - Mathematics and Statistics
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Question

Evaluate: `int_0^oo xe^-x.dx`

Sum

SolutionShow Solution

`int_0^∞ xe^-x.dx`

= `[x int e^-x.dx]_0^∞ - int_0^∞[d/dx (x) int e^-x.dx].dx`

= `[x((e^-x)/-1)]_0^∞ - int^∞ 1.(e^-x)/((-1)).dx`

= `[- x.e^x]_0^∞ + int_0^∞ e^-x.dx`

= `[x.e^-x]_0^∞ + [e^-x/-1]_0^∞`

= `[x.e^-x]_0^∞ - [-e^x]_0^∞`

= `[∞.e^-∞-0.e^-0] - [e^-∞-e^-0]`

= `[0 - 0] - [0-1/e^0]`

= `- [0-1/1]`

= 1. ...[∵ e0 = 1, e–x = 0, when x = ∞]

shaalaa.comMethods of Evaluation and Properties of Definite Integral Report Error Is there an error in this question or solution? Q 1.15Q 1.14Q 2.01Chapter 4: Definite Integration - Exercise 4.2 [Page 171]

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Balbharati Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State BoardChapter 4 Definite IntegrationExercise 4.2 | Q 1.15 | Page 171

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