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Grade 12Integral Calculus

if f ‘(x) = x+ b ,f(1) = 5 , f(2) = 13 find f(x)

taniska

11 Years agoGrade 12

1 Answer

Jitender Singh

11 Years ago

Ans:
Hello Student,
Please find answer to your question

$f'(x) = x + b$
$\frac{df(x)}{dx} = x + b$
$df(x) = (x + b)dx$
$\int df(x) = \int (x + b)dx$
$f(x) = \frac{x^2}{2} + bx + c$
$f(1) = \frac{1^2}{2} + b(1) + c$
$5 = \frac{1}{2} + b + c$
$b + c = \frac{9}{2}$ ….........(1)
$f(2) = \frac{2^2}{2} + b(2) + c$
$13 = 2 + 2b + c$
$2b + c = 11$ .........(2)
(2) – (1)
$b = 11 - \frac{9}{2} = \frac{13}{2}$
$c = \frac{9}{2} - \frac{13}{2} = -2$
$f(x) = \frac{x^2}{2} + \frac{13x}{2}-2$

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