If f '(x) = xx1x+x and f(1) = 52, then f(x) = log x + xx22 + ______ - Mathematics and Statistics

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If f '(x) = `1/"x" + "x"` and f(1) = `5/2`, then f(x) = log x + `"x"^2/2` + ______

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Solution

If f '(x) = `1/"x" + "x"` and f(1) = `5/2`, then f(x) = log x + `"x"^2/2` + 2

Explanation:

f(x) = ∫f '(x) dx

`= int (1/"x" + "x")` dx

f(x) = log |x| + `"x"^2/2 + "c"`   ...(i)

f(1) = `5/2`

f(1) = log 1 + `1^2/2` + c

∴ `5/2 = 0 + 1/2 + "c"`

∴ c = 2

∴ f(x) = log |x| + `"x"^2/2` + 2

Notes

The answer in the textbook is incorrect.

  Is there an error in this question or solution?
Chapter 5: Integration - Miscellaneous Exercise 5 [Page 138]

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Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 5 Integration
Miscellaneous Exercise 5 | Q 2.3 | Page 138

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