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

09.06.2025 00:24

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.

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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:

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