Find an antiderivative F(x) with F'(x) = f(x) and F(0) = 0. Is there only one possible solution? f(x) = 2x

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boske9s

2022-08-19

kwizerwa3w

Beginner2022-08-20Added 4 answers

An antiderivative F(x) with F'(x)=f(x)
F'(x)=f(x)
f(x)=2x
Now we take integration

\int F^{'} (x) d x = \int f (x) d x

F (x) = \int 2 x d x

F (x) = x^{2} + c

Where c is a constant. Now find out integration constant by using given initial condition F(0)=0

F (0) = {(0)}^{2} + c

0=c
Thus antiderivative become

F (x) = x^{2}

hence it is only one possible solution for given initial condition F(0)=0
Result:
An antiderivative is F(x) is

x^{2}

with given initial condition F(0)=0

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