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Calculate ∫ from 0 to 1 of (1/x) dx.
Calculate ∫ from 0 to 1 of (1/x) dx.
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Practice Questions
1 question
Q1
Calculate ∫ from 0 to 1 of (1/x) dx.
0
1
ln(1)
ln(2)
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The integral evaluates to [ln(x)] from 0 to 1 = ln(1) - ln(0) which diverges.
Questions & Step-by-step Solutions
1 item
Q
Q: Calculate ∫ from 0 to 1 of (1/x) dx.
Solution:
The integral evaluates to [ln(x)] from 0 to 1 = ln(1) - ln(0) which diverges.
Steps: 6
Show Steps
Step 1: Identify the integral you need to calculate, which is ∫ from 0 to 1 of (1/x) dx.
Step 2: Recognize that the integral of (1/x) is ln(x).
Step 3: Set up the evaluation of the integral using the limits from 0 to 1: [ln(x)] from 0 to 1.
Step 4: Substitute the upper limit (1) into ln(x): ln(1) = 0.
Step 5: Substitute the lower limit (0) into ln(x): ln(0) is undefined and approaches negative infinity.
Step 6: Calculate the result: ln(1) - ln(0) = 0 - (-∞), which diverges.
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