Given:

Required:
We need to find the trapezoid approximation and exact value.
Step-by-step explanation:

The given interval is {3,5} and n=4.
Consider the formula.

Substitute a=5, b=5, and n=4 in the formula,


Consider the trapezoid formula.







Consider the given integral.

Integrate the given integral.
![\int_3^5(6x^2+1)dx=[(6x^3)/(3)]^5_3+[x]^5_3](https://img.qammunity.org/2023/formulas/mathematics/college/llkq1ya13r0slc970wvsooeo0wkuvd8smv.png)
![=[2x^3]_3^5+[x]_3^5](https://img.qammunity.org/2023/formulas/mathematics/college/w5rc4y80a9a7m3s4jw5tjfj3bmnva6au0d.png)
![=[2(5)^3-2(3)^3]+[5-3]](https://img.qammunity.org/2023/formulas/mathematics/college/18t6kisgsooqgt5agnjtdsnesxqig6fe5e.png)


Final answer:

