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Determine the area under the curve y = e^x from x = 0 to x = 1.
Determine the area under the curve y = e^x from x = 0 to x = 1.
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Practice Questions
1 question
Q1
Determine the area under the curve y = e^x from x = 0 to x = 1.
e - 1
1
e
0
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The area under the curve y = e^x from 0 to 1 is given by ∫(from 0 to 1) e^x dx = [e^x] from 0 to 1 = e - 1.
Questions & Step-by-step Solutions
1 item
Q
Q: Determine the area under the curve y = e^x from x = 0 to x = 1.
Solution:
The area under the curve y = e^x from 0 to 1 is given by ∫(from 0 to 1) e^x dx = [e^x] from 0 to 1 = e - 1.
Steps: 8
Show Steps
Step 1: Identify the function you want to find the area under. In this case, the function is y = e^x.
Step 2: Determine the limits of integration. We want to find the area from x = 0 to x = 1.
Step 3: Set up the integral to calculate the area. This is written as ∫(from 0 to 1) e^x dx.
Step 4: Find the antiderivative of e^x. The antiderivative of e^x is e^x itself.
Step 5: Evaluate the antiderivative at the upper limit (x = 1) and the lower limit (x = 0). This means you calculate e^1 and e^0.
Step 6: Calculate e^1, which is e, and e^0, which is 1.
Step 7: Subtract the value at the lower limit from the value at the upper limit: e - 1.
Step 8: The result, e - 1, is the area under the curve from x = 0 to x = 1.
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