Evaluate: ∫x2-8x+7 dx - Mathematics and Statistics

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Sum

Evaluate: `int sqrt(x^2 - 8x + 7)` dx

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Solution

Let I = `int sqrt(x^2 − 8x + 7)` dx

`"I" = int sqrt(x^2 − 8x + 16 − 9)` dx

`"I" = int sqrt((x^2 − 8x + 16) − 9)` dx

`"I" = int sqrt((x − 4)^2 − (3)^2)` dx

∴ `int sqrt(x^2 − a^2)  "dx" = x/2 sqrt(x^2 − a^2) − a^2/2 log |x + sqrt(x^2 − a^2)| + c` 

`"I" = (x − 4)/2 sqrt((x - 4)^2 − (3)^2) − (3)^2/2log |(x − 4) + sqrt((x − 4)^2 − (3)^2)| + c`

`"I" = (x − 4)/2 sqrt(x^2 − 8x + 7) − 9/2 log |(x − 4) + sqrt(x^2 − 8x + 7)| + 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) vii) | Page 139

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