Evaluate: ∫ex dx - Mathematics and Statistics

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Sum

Evaluate: `int "e"^sqrt"x"` dx

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Solution

Let I = `int "e"^sqrt"x"` dx

Put `sqrt"x"` = t

∴ x = t2

∴ dx = 2t  dt

∴ I = `int "e"^"t" * "2t"`dt

`= 2 int "t" * "e"^"t" * "dt"`

`= 2 ["t" int "e"^"t" "dt" - int {"d"/"dx" ("t") int "e"^"t" * "dt"}"dt"]`

`= 2 ["t" * "e"^"t" - int 1 * "e"^"t" "dt"]`

`= 2("te"^"t" - "e"^"t")` + c

`= 2"e"^"t" ("t - 1")` + c

∴ I = `2"e"^sqrt"x" (sqrt"x" - 1)` + c

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Chapter 5: Integration - MISCELLANEOUS EXERCISE - 5 [Page 139]

APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 5 Integration
MISCELLANEOUS EXERCISE - 5 | Q IV. 4) v) | Page 139

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