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The question asks to evaluate the integral \( \int_2^4 (2x + 3) dx \).

Let's solve it step-by-step:

### Step 1: Find the antiderivative
The function to integrate is \( 2x + 3 \). Its antiderivative is:
\[
\int (2x + 3) dx = x^2 + 3x + C
\]

### Step 2: Apply the limits of integration
Now, we apply the limits \( x = 4 \) and \( x = 2 \):

\[
\left[ x^2 + 3x \right]_2^4 = \left( 4^2 + 3(4) \right) - \left( 2^2 + 3(2) \right)
\]

### Step 3: Calculate the values
\[
\left( 16 + 12 \right) - \left( 4 + 6 \right) = 28 - 10 = 18
\]

So, the value of the integral is \( 18 \), corresponding to option **d**.

Would you like any further details or explanations? 

Here are some related questions:
1. How would you solve this integral if the limits were different?
2. What is the geometric meaning of this integral?
3. How do you find the antiderivative of more complex functions?
4. What happens if the integrand includes trigonometric functions?
5. How can integration by parts be used in other cases?

**Tip:** Always verify if the function can be simplified before integrating—it can save time!

Evaluate the integral ∫(2x + 3)dx from 2 to 4.

Learn how to solve the definite integral ∫(2x + 3)dx from 2 to 4 with a step-by-step solution. This problem covers key calculus concepts, including finding the antiderivative and applying the limits of integration. Suitable for students in Grades 10-12.

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