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What is the area under the curve y = 1/x from x = 1 to x = 2?

Practice Questions

Q1
What is the area under the curve y = 1/x from x = 1 to x = 2?
  1. ln(2)
  2. 1
  3. ln(2) - 1
  4. 0

Questions & Step-by-Step Solutions

What is the area under the curve y = 1/x from x = 1 to x = 2?
  • Step 1: Identify the function we are working with, which is y = 1/x.
  • Step 2: Determine the limits of integration, which are from x = 1 to x = 2.
  • Step 3: Set up the integral to find the area under the curve: ∫(from 1 to 2) (1/x) dx.
  • Step 4: Calculate the integral of 1/x, which is ln(x).
  • Step 5: Evaluate the integral from the lower limit (1) to the upper limit (2): [ln(x)] from 1 to 2.
  • Step 6: Substitute the limits into the evaluated integral: ln(2) - ln(1).
  • Step 7: Simplify the expression: ln(1) is 0, so the area is ln(2).
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