math, calculus

if f(1)=12 and f' is continuous, what is the value of f(4)?

integral from 1 to 4 of f'(x)dx = 17

IF the integral of f'(x) dx from 1 to 4 is 17, as you say, then the function f(x), which is the integral with an arbitrary constant, changes by 17 from 1 to 4. Then the value of f(x) at x=4 must be 12 + 17 = 29.

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