Integral of Equation Involving  
 (Make it your own with coefficients and constants.)

Let's consider the integral of the following equation:

\[ f(x) = 3x^2 - 5x + 4 \]

We want to find the integral of this function with respect to \( x \):

\[
\int (3x^2 - 5x + 4) \, dx
\]

### Steps to Solve:

1. **Integrate each term separately**:
   - The integral of \( 3x^2 \) is \( x^3 \).
   - The integral of \( -5x \) is \( -\frac{5}{2}x^2 \).
   - The integral of \( 4 \) is \( 4x \).

2. **Combine the results**:
   \[
   \int (3x^2 - 5x + 4) \, dx = x^3 - \frac{5}{2}x^2 + 4x + C
   \]
   where \( C \) is the constant of integration.

### Final Result:
\[
\int (3x^2 - 5x + 4) \, dx = x^3 - \frac{5}{2}x^2 + 4x + C
\]

Would you like more details on any specific part of this process, or do you have any questions? Here are some related questions you might consider:

1. How do you find the definite integral of this function over a specific interval?
2. What is the geometric interpretation of the integral in this case?
3. How can you apply integration to solve real-world problems?
4. What techniques can be used for integrating more complex functions?
5. Can you explain the concept of the constant of integration \( C \)? 

**Tip:** When integrating, always double-check your work by differentiating your result to see if you obtain the original function.

Discover the step-by-step solution to the integral of the polynomial function 3x^2 - 5x + 4. This explanation covers key calculus concepts and integration techniques, suitable for students in Grades 11-12.

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