The integral given is:

$I = \int_0^2 \frac{e^x}{1+x^2}\,dx$

The problem specifies $n = 10$, which might suggest the use of a numerical method to approximate the value of the integral, such as Simpson's rule, the trapezoidal rule, or simply specifying the number of intervals for numerical integration.

Would you like me to proceed with a numerical approximation using $n = 10$, or would you prefer a different method for evaluating this integral?

Let me know, and I can provide more details!

Here are 5 related questions to consider:

1. What is the significance of increasing $n$ in numerical integration methods like Simpson’s rule?
2. How does Simpson’s rule differ from the trapezoidal rule in terms of accuracy?
3. What is the error estimation for Simpson’s rule when approximating integrals?
4. Could this integral be computed using a series expansion for $e^x$?
5. How does the presence of $1 + x^2$ in the denominator affect the integrand behavior?

Tip: For better accuracy in numerical integration, especially with complex functions, increasing the number of subintervals $n$ can lead to significantly more accurate results!