The integral you've provided is:

\[
\int_0^{x} 1 \, \mathrm{d}x
\]

To solve this, we integrate the constant \( 1 \) over the interval from \( 0 \) to \( x \).

### Solution:
1. Since the integrand is \( 1 \), integrating \( 1 \) with respect to \( x \) yields \( x \):
   \[
   \int 1 \, \mathrm{d}x = x
   \]

2. Now, we evaluate this from \( 0 \) to \( x \):
   \[
   \int_0^x 1 \, \mathrm{d}x = \left[ x \right]_0^x
   \]

3. Substitute the limits:
   \[
   = x - 0 = x
   \]

### Final Answer:
\[
\int_0^{x} 1 \, \mathrm{d}x = x
\]

Would you like further details or have any questions?

Here are some related questions that expand on this concept:

1. What happens when we integrate a constant other than 1 over a similar interval?
2. How would this integral change if the limits were from \( a \) to \( b \) instead of \( 0 \) to \( x \)?
3. How do definite and indefinite integrals differ conceptually?
4. What are some applications of constant integrals in real-world contexts?
5. How does this integral represent the area under a constant function?

**Tip:** Integrating a constant over an interval gives the length of the interval times the value of the constant, which represents the area of a rectangle.

Learn how to evaluate the definite integral of a constant function, \( \int_0^{x} 1 \, dx \), with a step-by-step solution. This problem explores key concepts in calculus, including definite integration and the Fundamental Theorem of Calculus. Ideal for students in Grades 11-12.

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