Question: Evaluate the integral ∫ from 0 to 1 of e^x dx.
Options:
e - 1
e
1
0
Correct Answer: e - 1
Solution:
The integral evaluates to [e^x] from 0 to 1 = e - 1.
Evaluate the integral ∫ from 0 to 1 of e^x dx.
Practice Questions
Q1
Evaluate the integral ∫ from 0 to 1 of e^x dx.
e - 1
e
1
0
Questions & Step-by-Step Solutions
Evaluate the integral ∫ 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 exponential function e^x.
Fundamental Theorem of Calculus – The theorem that connects differentiation and integration, allowing evaluation of definite integrals using antiderivatives.
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