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What is the definite integral of x^x from 0 to 2?

12.06.2025 00:20

What is the definite integral of x^x from 0 to 2?

I=∫02xx dxI = \int_0^2 x^x \, dx

The definite integral of xxx^x from 0 to 2 is approximately 2.83392.8339, with a very small error estimate of about 2.66×10−102.66 \times 10^{-10}. ​

I can compute this numerically for you. Let's do that.

Why do programmers choose to write their own code instead of using code that is already available online?

The integral of xxx^x from 0 to 2 does not have a simple closed-form solution using elementary functions. However, it can be computed numerically. The definite integral you're asking for is: