The area bounded by the curve `y={x}` with the x-axis from `x=pi` to `x=3.8` is `((pi)/(2)-a)(b-pi)` sq. units, then the value of `b-a` is equal to (where `{.}` denotes the fractional part function)

Answer

To solve the problem, we need to find the area bounded by the curve \( y = \{x\} \) (the fractional part of \( x \)) with the x-axis from \( x = \pi \) to \( x = 3.8 \).

### Step-by-step Solution:

1. **Understanding the Function**:
The fractional part function \( \{x\} \) can be expressed as:
\[ \{x\} = x - \lfloor x \rfloor \]
where \( \lfloor x \rfloor \) is the greatest integer less than or equal to \( x \).

2. **Identifying the Interval**:
We are interested in the interval from \( x = \pi \) to \( x = 3.8 \). Since \( \pi \approx 3.14 \), we can see that:
- For \( x = \pi \), \( \lfloor \pi \rfloor = 3 \).
- For \( x = 3.8 \), \( \lfloor 3.8 \rfloor = 3 \).

3. **Calculating the Function Values**:
- At \( x = \pi \):
\[ y = \{\pi\} = \pi - 3 \]
- At \( x = 3.8 \):
\[ y = \{3.8\} = 3.8 - 3 = 0.8 \]

4. **Finding the Area**:
The area between the curve and the x-axis from \( x = \pi \) to \( x = 3.8 \) can be visualized as a trapezium with heights \( \{\pi\} \) and \( \{3.8\} \) and a base length of \( 3.8 - \pi \).
- The area \( A \) can be calculated as:
\[ A = \frac{1}{2} \times (\{\pi\} + \{3.8\}) \times (3.8 - \pi) \]
Substituting the values:
\[ A = \frac{1}{2} \times ((\pi - 3) + 0.8) \times (3.8 - \pi) \]
Simplifying:
\[ A = \frac{1}{2} \times (\pi - 2.2) \times (3.8 - \pi) \]

5. **Expressing the Area**:
The area is given in the problem as:
\[ A = \left(\frac{\pi}{2} - a\right)(b - \pi) \]
We can compare the two expressions for the area to find \( a \) and \( b \).

6. **Comparing the Expressions**:
From the area expression:
\[ \frac{1}{2} \times (\pi - 2.2) \times (3.8 - \pi) = \left(\frac{\pi}{2} - a\right)(b - \pi) \]
We can deduce:
- \( a = 1.1 \)
- \( b = 3.8 \)

7. **Finding \( b - a \)**:
Finally, we calculate:
\[ b - a = 3.8 - 1.1 = 2.7 \]

### Conclusion:
The value of \( b - a \) is \( 2.7 \).