Consider the integral | (2x2 + 3x + 2) dæ (a) Find the Riemann sum for this integral using the right-hand sums for n = 3. (b) Find the Riemann sum for this same integral, using the left-hand sums for n =

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I don't know how to solve the attached Reiman sum question.

**Consider the integral**

\[
\int_{0}^{6} (2x^2 + 3x + 2) \, dx
\]

(a) Find the Riemann sum for this integral using the right-hand sums for \( n = 3 \).

(b) Find the Riemann sum for this same integral, using the left-hand sums for \( n = 3 \).

---

In this exercise, you are asked to approximate the value of the definite integral of the polynomial function \(2x^2 + 3x + 2\) over the interval from 0 to 6. You will calculate Riemann sums using both right-hand and left-hand approaches with 3 subintervals.

1. **Right-Hand Riemann Sum:**
   - Divide the interval \([0, 6]\) into 3 equal subintervals.
   - For each subinterval, evaluate the function at the right endpoint to estimate the area.

2. **Left-Hand Riemann Sum:**
   - Similarly, divide the interval \([0, 6]\) into 3 subintervals.
   - For each subinterval, evaluate the function at the left endpoint to estimate the area.

This activity helps in understanding how the choice of endpoints affects the approximation of the integral.
Transcribed Image Text:**Consider the integral** \[ \int_{0}^{6} (2x^2 + 3x + 2) \, dx \] (a) Find the Riemann sum for this integral using the right-hand sums for \( n = 3 \). (b) Find the Riemann sum for this same integral, using the left-hand sums for \( n = 3 \). --- In this exercise, you are asked to approximate the value of the definite integral of the polynomial function \(2x^2 + 3x + 2\) over the interval from 0 to 6. You will calculate Riemann sums using both right-hand and left-hand approaches with 3 subintervals. 1. **Right-Hand Riemann Sum:** - Divide the interval \([0, 6]\) into 3 equal subintervals. - For each subinterval, evaluate the function at the right endpoint to estimate the area. 2. **Left-Hand Riemann Sum:** - Similarly, divide the interval \([0, 6]\) into 3 subintervals. - For each subinterval, evaluate the function at the left endpoint to estimate the area. This activity helps in understanding how the choice of endpoints affects the approximation of the integral.
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