# Fill in the Blank. If f '(x) = 1x+x and f(1) = 52, then f(x) = log x + x22 + - Mathematics and Statistics

Fill in the Blanks

Fill in the Blank.

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

#### 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

[Note: Answer in the textbook is incorrect.]

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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 2.3 | Page 138