The formula for f , the specific antiderivative of f is F(u) = 4㏑(u) + u²/2 + 11/2 .
In the question ,
it is given that ,
the function f(u) is f(u) = 4/u + u and f(1) = 6 ,
to find the antiderivative of f , we integrate it with respect to u ,
∫f(u) = 4∫(1/u)du + ∫u.du
On integrating ,
we get ,
F(u) = 4㏑(u) + u²/2 + c ......equation(1)
Substituting the value of u = 1 in equation(1) ,
we get ,
F(1) = 4㏑(1) + 1/2 + c
6 = 0 + 1/2 + c
c = 6 - 1/2
c = 11/2 .
Now , substituting the value of c = 11/2 in equation(1) , we get
F(u) = 4㏑(u) + u²/2 + 11/2
Therefore , the formula for f is F(u) = 4㏑(u) + u²/2 + 11/2 .
The given question is incomplete , the complete question is
Write a formula for f, the specific antiderivative of f.
f(u) = 4/u + u ; F(1) = 6 .
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