Please help with n=32 **Using Simpson's Rule for Numerical Integration**In this section, we'll apply Simpson's Rule to approximate the integral of the function \( \int_0^8 (3x^5 - 2x^3) \, dx \), with the exact value being 129,024. We'll provide a table showing approximations and errors for different segment values \( n = 4, 8, 16, \) and \( 32 \).**Table of Approximations and Errors**| \( n \) | \( T(n) \) | \( S(n) \) | Absolute Error in \( T(n) \) | Absolute Error in \( S(n) \) ||---------|-----------|----------|-------------------------|-------------------------|| 4 | 149,120 | — | 20,096 | — || 8 | 134,096 | 129,088 | 5,072 | 64 || 16 | 130,295 | 129,028 | 1,271 | 4 || 32 | 129,341.9 | 129,024.25 | 317.9 | 0.25 |**Explanation:**- \( T(n) \) refers to the approximation using the Trapezoidal Rule.- \( S(n) \) refers to the approximation using Simpson's Rule.- The absolute errors for each method are calculated by comparing the approximation with the exact integral value \( 129,024 \).Simpson's Rule generally provides a more accurate approximation, as evidenced by smaller errors compared to the Trapezoidal Rule, particularly as \( n \) increases.

Given Data: Given exact value of the integral is ∫083x5-2x3dx=129024…

Apply Simpson's Rule to the following integral. It is easiest to obtain the Simpson's Rule Make a table showing the approximations and errors for n = 4, 8, 16, and 32. The exact 8 n 0 1125- *** (3x5 - 2x³) dx = 129,024 4 8 16 32 T(n) 149120 134096 130295 129341.9 S(n) 129088 129028 129024.25 Absolute Error in T(n) 20096 5072 1271 317.9 --- ... Absolute Error in S(n) - 64 4 0.25