Work through the following steps to approximate $\int_{1}^{10}\left(x^{2}+6\right) d x$
a) We know that $a=$ and $b=10$
b) Using 3 subintervals, $\Delta x=3$
Part 2 of 4
c) Assume that the sample points in each interval are right endpoints. Find the sample points:
\[
x_{1}=
\]
\[
x_{2}=
\]
\[
x_{3}=
\]

Step 1 ：Given the function \(f(x) = x^2 + 6\) and the interval from 1 to 10, we are asked to approximate the definite integral using 3 subintervals and right endpoints.

Step 2 ：First, calculate the width of each subinterval, which is \(\Delta x = \frac{b - a}{n}\) where \(a\) is the lower limit of the integral, \(b\) is the upper limit, and \(n\) is the number of subintervals. In this case, \(a = 1\), \(b = 10\), and \(n = 3\). So, \(\Delta x = 3.0\).

Step 3 ：Next, find the sample points, which are the right endpoints of each subinterval. The first sample point \(x_1\) is \(a + \Delta x\), the second sample point \(x_2\) is \(a + 2\Delta x\), and the third sample point \(x_3\) is \(a + 3\Delta x\).

Step 4 ：Substituting the values, we get \(x_1 = 4.0\), \(x_2 = 7.0\), and \(x_3 = 10.0\).

Step 5 ：\(\boxed{\text{The sample points are } x_{1}=4, x_{2}=7, \text{ and } x_{3}=10}\)