# A doubt of Integrals !

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

Note by Rishu Jaar
3 years, 6 months ago

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- 3 years, 6 months ago

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

- 3 years, 6 months ago

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

- 3 years, 6 months ago

Thanks , could you provide a link?

- 3 years, 6 months ago

Trapezium Rule

- 3 years, 6 months ago

Thanks!

- 3 years, 6 months ago

@Rishabh Cool and others please give a proof !

- 3 years, 6 months ago

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.

- 3 years, 6 months ago

Oh can you explain more.

- 3 years, 6 months ago

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

- 3 years, 6 months ago

Ok sure.

- 3 years, 6 months ago

@RISHU Jaar It's in the new section.

- 3 years, 6 months ago

Done.

- 3 years, 6 months ago