What is the exact value of the integral of e raised to the x from 0 to π?

To find the exact value of the integral of e^x from 0 to π, we first need to evaluate the integral itself. The integral of e^x with respect to x is e^x, which is one of the fundamental properties of the exponential function.

When we are looking at the definite integral from 0 to π, we can express this as:

∫(from 0 to π) e^x dx = [e^x] evaluated from 0 to π.

Now, we will apply the limits of integration. We first evaluate e^x at the upper limit, which is π:

e^π

Next, we evaluate e^x at the lower limit, which is 0:

e^0 = 1

Now we subtract the value at the lower limit from the value at the upper limit:

e^π - 1.

This gives us the exact value of the integral. Therefore, the correct answer, reflecting the evaluation of the definite integral, is indeed e^π - 1.

This matches the response given, confirming it as the precise evaluation of the integral.