Calculate ∫_0^1 (e^x) dx.

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Question: Calculate ∫_0^1 (e^x) dx.

Options:

Correct Answer: e - 1

Solution:

∫_0^1 e^x dx = [e^x] from 0 to 1 = e - 1.

Calculate ∫_0^1 (e^x) dx.

Calculate ∫_0^1 (e^x) dx.

Step 1: Identify the integral you need to calculate, which is ∫_0^1 e^x dx.
Step 2: Find the antiderivative of e^x. The antiderivative of e^x is e^x itself.
Step 3: Write down the antiderivative with limits: [e^x] from 0 to 1.
Step 4: Evaluate the antiderivative at the upper limit (1): e^1 = e.
Step 5: Evaluate the antiderivative at the lower limit (0): e^0 = 1.
Step 6: Subtract the lower limit result from the upper limit result: e - 1.
Step 7: Write the final answer: ∫_0^1 e^x dx = e - 1.

Definite Integral – The question tests the ability to compute a definite integral of the exponential function over a specified interval.
Fundamental Theorem of Calculus – It assesses understanding of how to apply the Fundamental Theorem of Calculus to evaluate integrals.