If `int_(a)^(b)f(dx)dx=l_(1), int_(a)^(b)g(x)dx = l_(2)` then :

Answer

To solve the problem, we start with the given information:

1. \( \int_{a}^{b} f(x) \, dx = l_1 \)
2. \( \int_{a}^{b} g(x) \, dx = l_2 \)

We need to analyze the options provided based on these integrals.

### Step 1: Evaluate the integral of the sum of functions

Using the property of integrals, we know that:

\[ \int_{a}^{b} (f(x) + g(x)) \, dx = \int_{a}^{b} f(x) \, dx + \int_{a}^{b} g(x) \, dx \]

Substituting the known values:

\[ \int_{a}^{b} (f(x) + g(x)) \, dx = l_1 + l_2 \]

### Step 2: Evaluate the integral of the product of functions

For the product of two functions, we cannot directly express the integral as a simple product of the integrals. Therefore, we cannot say:

\[ \int_{a}^{b} f(x) g(x) \, dx = l_1 l_2 \]

This statement is generally false unless \( f(x) \) and \( g(x) \) are specific types of functions (like constants).

### Step 3: Evaluate the integral of the quotient of functions

Similarly, for the quotient of two functions, we cannot express the integral in terms of the integrals of the individual functions:

\[ \int_{a}^{b} \frac{f(x)}{g(x)} \, dx \neq \frac{l_1}{l_2} \]

This statement is also generally false unless specific conditions are met.

### Conclusion

Based on the evaluations:

1. The integral of the sum is \( l_1 + l_2 \).
2. The integral of the product and the integral of the quotient cannot be expressed as simple products or ratios of \( l_1 \) and \( l_2 \).

Thus, the correct conclusion is:

\[ \int_{a}^{b} (f(x) + g(x)) \, dx = l_1 + l_2 \]

### Final Answer

The correct option is:

\[ \int_{a}^{b} (f(x) + g(x)) \, dx = l_1 + l_2 \]