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Find the value of the definite integral : \[ \displaystyle \int_0^1( 1+e^{-x^{2}} )dx \]

Note by Rishu Jaar 1 year, 2 months ago

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2 \times 3

2^{34}

a_{i-1}

\frac{2}{3}

\sqrt{2}

\sum_{i=1}^3

\sin \theta

\boxed{123}

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Read Error function.

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@Pi Han Goh , thank you , its a jee 1981 question but didn't knew the maths involved was so higher.

Then you can only evaluate it using numerical methods, like trapezoidal rule or Simpson's rule.

@Pi Han Goh – Thanks , could you provide a link?

@Rishu Jaar – Trapezium Rule

@Pi Han Goh – Thanks!

@Rishabh Cool and others please give a proof !

If, by value, you mean the area under the curve from 0 to 1, the solution would be 1/2 sqrt(π) • e • rf(1) + 1. This is simply found by removing the parentheses, taking the derivative, and then solving from there as usual.

Oh can you explain more.

Yes - I'll post a new discussion called JEE 1981 Int Calc with the information enclosed. I need my LaTeX!

@Hunter Edwards – Ok sure.

@Rishu Jaar – @RISHU Jaar It's in the new section.

@Hunter Edwards – Done.

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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

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TopNewestRead Error function.

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@Pi Han Goh , thank you , its a jee 1981 question but didn't knew the maths involved was so higher.

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Then you can only evaluate it using numerical methods, like trapezoidal rule or Simpson's rule.

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Trapezium Rule

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@Rishabh Cool and others please give a proof !

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If, by value, you mean the area under the curve from 0 to 1, the solution would be 1/2 sqrt(π) • e • rf(1) + 1. This is simply found by removing the parentheses, taking the derivative, and then solving from there as usual.

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Oh can you explain more.

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Yes - I'll post a new discussion called JEE 1981 Int Calc with the information enclosed. I need my LaTeX!

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@RISHU Jaar It's in the new section.

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