# Evaluate: If f '(x) = x and f(1) = 2, then find the value of f(x). - Mathematics and Statistics

Sum

Evaluate: If f '(x) = sqrt"x" and f(1) = 2, then find the value of f(x).

#### Solution

f '(x) = sqrt"x"     ....[Given]

f(x) = ∫ f '(x)

= int sqrt"x" dx

= int "x"^(1/2) dx

= "x"^(3/2)/(3/2) + c

∴ f(x) = 2/3 "x"^(3/2) + "c" ...(i)

Now, f(1) = 2      ....[Given]

∴ 2/3 (1)^(3/2) + "c" = 2

∴ c = 2 - 2/3

∴ c = 4/3

∴ f(x) = 2/3 "x"^(3/2) + 4/3

Concept: Methods of Integration: Integration by Substitution
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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 4.1 | Page 138