What is $F (x) = \int e^{x - 2} - x d x$ $F(x) = int e^(x-2) - x dx$ if $F (0) = 1$ $F(0) = 1$ ?

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Answer 1 · 2017-04-28T10:27:35

$F (x) = e^{x - 2} - \frac{1}{2} x^{2} + 1 - e^{- 2}$ $F(x) = e^(x-2) - 1/2x^2 + 1 - e^(-2)$

We have:

$F(x) = int \ e^(x-2) - x \ dx$

Integrating wrt $x$ we get:

$F(x) = e^(x-2) - 1/2x^2 + C$

But we know that $F(0)=1$ , and so:

$e^(0-2) - 0 + C = 1$
$:. e^(-2) + C = 1$
$:. C = 1 - e^(-2)$

Hence,

$F(x) = e^(x-2) - 1/2x^2 + 1 - e^(-2)$

What is F(x) = int e^(x-2) - x dxF(x)=∫ex−2−xdxF(x) = int e^(x-2) - x dx if F(0) = 1 F(0)=1F(0) = 1 ?