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STEP 3: Evaluate each term and find the sum.

[tex]\[
\begin{array}{l}
= (0.5)(2) + (0.5)(2.25) + (0.5)(3) + (0.5)(4.25) \\
\leftarrow \begin{array}{l}
f(x) = x^2 + 2, \\
f(1) = 1^2 + 2 = 3
\end{array} \\
= 0.5(2 + 2.25 + 3 + 4.25) \\
= 0.5(11.5) \\
= 5.75
\end{array}
\][/tex]

The area under the curve is about 5.75 square units.



Answer :

GinnyAnswer
To follow the steps to evaluate each term and find the sum accurately, we will break down the given expression and perform calculations for each term individually:

Let's start with the given expression:
[tex]\[ \left(0.5 \cdot 2\right) + \left(0.5 \cdot 2.25\right) + \left(0.5 \cdot 3\right) + \left(0.5 \cdot 4.25\right) \][/tex]

### Step-by-Step Evaluation:

1. Evaluate the first term:
[tex]\[ 0.5 \cdot 2 = 1.0 \][/tex]

2. Evaluate the second term:
[tex]\[ 0.5 \cdot 2.25 = 1.125 \][/tex]

3. Evaluate the third term:
[tex]\[ 0.5 \cdot 3 = 1.5 \][/tex]

4. Evaluate the fourth term:
[tex]\[ 0.5 \cdot 4.25 = 2.125 \][/tex]

### Sum the Calculated Terms:

Adding all the evaluated terms together:
[tex]\[ 1.0 + 1.125 + 1.5 + 2.125 \][/tex]

Let's sum them up step-by-step:
- [tex]\(1.0 + 1.125 = 2.125\)[/tex]
- [tex]\(2.125 + 1.5 = 3.625\)[/tex]
- [tex]\(3.625 + 2.125 = 5.75\)[/tex]

So, the sum of the terms is [tex]\(5.75\)[/tex].

### Conclusion:

The area under the curve is approximately 5.75 square units.

Therefore, through the step-by-step evaluation of each term and summing them, we have determined that the sum is 5.75.

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