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If f^(prime)(x)=x+b ,\ \ f(1)=5,\ \ f(2)...

If `f^(prime)(x)=x+b ,\ \ f(1)=5,\ \ f(2)=13 ,` find `f(x)` .

Text Solution

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`intf'(x)\dx=(x^2)/(2)+bx+C`

Given that, `f(1)=5, f(2)=13`

`(1^2)/(2)+b+C=5`

`b+C=9/2`


`(2^2)/(2)+2b+C=13`

`2+2b+C=13`

`b+9/2=11`

`b=13/2`

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