New user? Sign up

Existing user? Sign in

\[ \large g(x) = e^x \int_0^1 e^x g(x) \, dx \]

Find \(g(0) \).

Note by D K 1 year, 6 months ago

Easy Math Editor

*italics*

_italics_

**bold**

__bold__

- bulleted- list

1. numbered2. list

paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)

> This is a quote

This is a quote

# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

2 \times 3

2^{34}

a_{i-1}

\frac{2}{3}

\sqrt{2}

\sum_{i=1}^3

\sin \theta

\boxed{123}

Sort by:

\[\large g(x)=e^x \underbrace{\displaystyle\int_0^1e^xg(x)\mathrm{d}x}_{\text{Constant=C}}=Ce^x\]

\[C=\displaystyle\int_0^1e^x(Ce^x)\mathrm{d}x=\frac C2(e^2-1)\implies C=0\]

Hence \(\large g(x)=0\forall x\in \mathbb R\)

Hence \(g(0)=0\).

Log in to reply

Explain, how is that a constant?

Any definite integral with constant bounds is a constant.

Couldn't \(g(x) = 0?\) Just seems like \(g(0) = 0\) then.

g(0)=0

Problem Loading...

Note Loading...

Set Loading...

Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

Sort by:

TopNewest\[\large g(x)=e^x \underbrace{\displaystyle\int_0^1e^xg(x)\mathrm{d}x}_{\text{Constant=C}}=Ce^x\]

\[C=\displaystyle\int_0^1e^x(Ce^x)\mathrm{d}x=\frac C2(e^2-1)\implies C=0\]

Hence \(\large g(x)=0\forall x\in \mathbb R\)

Hence \(g(0)=0\).

Log in to reply

Explain, how is that a constant?

Log in to reply

Any definite integral with constant bounds is a constant.

Log in to reply

Couldn't \(g(x) = 0?\) Just seems like \(g(0) = 0\) then.

Log in to reply

g(0)=0

Log in to reply