Evaluate the following :
`int_(5)^(6)e^(x)dx`

Answer

To evaluate the integral \(\int_{5}^{6} e^{x} \, dx\), we will follow these steps:

### Step 1: Identify the integral
We need to evaluate the definite integral of the function \(e^x\) from \(x = 5\) to \(x = 6\).

### Step 2: Find the antiderivative
The antiderivative of \(e^x\) is \(e^x\). This means:
\[ \int e^{x} \, dx = e^{x} + C \]
where \(C\) is the constant of integration.

### Step 3: Apply the limits of integration
Now we will evaluate the definite integral using the limits from 5 to 6:
\[ \int_{5}^{6} e^{x} \, dx = \left[ e^{x} \right]_{5}^{6} \]
This means we will calculate \(e^{6}\) and \(e^{5}\) and then find their difference.

### Step 4: Calculate the values at the limits
Now we compute:
\[ \left[ e^{x} \right]_{5}^{6} = e^{6} - e^{5} \]

### Step 5: Final result
Thus, the value of the integral is:
\[ e^{6} - e^{5} \]

### Summary of the solution
The evaluated integral \(\int_{5}^{6} e^{x} \, dx\) is:
\[ e^{6} - e^{5} \]