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Find the area under the curve y = e^x from x = 0 to x = 1.
Find the area under the curve y = e^x from x = 0 to x = 1.
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Practice Questions
1 question
Q1
Find the area under the curve y = e^x from x = 0 to x = 1.
e - 1
1
e
0
Show Solution
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The area is given by the integral from 0 to 1 of e^x dx. This evaluates to [e^x] from 0 to 1 = e - 1.
Questions & Step-by-step Solutions
1 item
Q
Q: Find the area under the curve y = e^x from x = 0 to x = 1.
Solution:
The area is given by the integral from 0 to 1 of e^x dx. This evaluates to [e^x] from 0 to 1 = e - 1.
Steps: 7
Show Steps
Step 1: Identify the function you want to find the area under. In this case, it is y = e^x.
Step 2: Determine the limits for the area you want to calculate. Here, the limits are from x = 0 to x = 1.
Step 3: Set up the integral to find the area. This is written as the integral from 0 to 1 of e^x dx.
Step 4: Calculate the integral. The integral of e^x is e^x itself.
Step 5: Evaluate the integral at the upper limit (x = 1) and the lower limit (x = 0). This means you calculate e^1 - e^0.
Step 6: Simplify the result. e^1 is just e, and e^0 is 1, so you get e - 1.
Step 7: Conclude that the area under the curve from x = 0 to x = 1 is e - 1.
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