Evaluate ∫ from 0 to 1 of e^x dx.

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Question: Evaluate ∫ from 0 to 1 of e^x dx.

Options:

Correct Answer: e - 1

Solution:

The integral evaluates to [e^x] from 0 to 1 = e - 1.

Evaluate ∫ from 0 to 1 of e^x dx.

Evaluate ∫ from 0 to 1 of e^x dx.

Correct Answer: e - 1

Step 1: Identify the integral you need to evaluate, which is ∫ from 0 to 1 of 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: Substitute the upper limit (1) into the antiderivative: e^1 = e.
Step 5: Substitute the lower limit (0) into the antiderivative: e^0 = 1.
Step 6: Calculate the result by subtracting the lower limit result from the upper limit result: e - 1.
Step 7: Write the final answer: The integral evaluates to e - 1.

Definite Integral – The process of calculating the area under the curve of a function between two specified limits.
Exponential Function – Understanding the properties and behavior of the function e^x, particularly its integral.