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

Question

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

1 Answer

Impact of this question

2208 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-08T13:39:33

the antiderivative of $f (x) = e^{x} - e^{- (2 x)}$ $f(x) = e^x - e^-(2x)$

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

that is to say that the derivative of $F (x)$ $F(x)$ is equal to $f (x)$ $f(x)$
$= \frac{d}{d x} (e^{x} - \frac{e^{2 x}}{2} + C) = e^{x} - e^{- 2 x}$ $= d/dx (e^x - e^(2x) / 2 + C) = e^x - e^(-2x)$

now we just need to find C to get the total antiderivative of $f (x)$ $f(x)$
and we can use the fact that at $x = 0$ $x = 0$ the value comes out as -2
$therefore f( 0) = -2$

therefore
$e^0 - e^(2*0) / 2 + C = -2$
$= 1-1/2 + C = -2$

therefore,
$C = -2 1/2$
=
therefore, the entire function becomes
$e^x - e^(2x) / 2 - 2 1/2$

Science

Math

Humanities

... and beyond

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

1 Answer

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

What is f(x) = int e^x-e^(-2x) dxf(x)=∫ex−e−2xdxf(x) = int e^x-e^(-2x) dx if f(0)=-2 f(0)=−2f(0)=-2 ?

1 Answer

Related questions

Impact of this question

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