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

Sum

Evaluate: `int sqrt("x"^2 - 8"x" + 7)` dx

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Solution

Let I = `int sqrt("x"^2 - 8"x" + 7)` dx

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

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

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

∴ I = `("x" - 4)/2 sqrt("x"^2 - 8"x" + 7) + 9/2 log |("x - 4") + sqrt("x"^2 - 8"x" + 7)|` + c

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APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 5 Integration
Miscellaneous Exercise 5 | Q 4.4 | Page 139
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