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What is the value of the integral ∫(0 to 1) x^2 dx?

Practice Questions

Q1
What is the value of the integral ∫(0 to 1) x^2 dx?
  1. 1/3
  2. 1/2
  3. 1/4
  4. 1

Questions & Step-by-Step Solutions

What is the value of the integral ∫(0 to 1) x^2 dx?
  • Step 1: Identify the integral you need to solve, which is ∫(0 to 1) x^2 dx.
  • Step 2: Find the antiderivative of x^2. The antiderivative is (x^3)/3.
  • Step 3: Write down the antiderivative with limits: [(x^3)/3] from 0 to 1.
  • Step 4: Substitute the upper limit (1) into the antiderivative: (1^3)/3 = 1/3.
  • Step 5: Substitute the lower limit (0) into the antiderivative: (0^3)/3 = 0.
  • Step 6: Subtract the value from the lower limit from the value from the upper limit: (1/3) - (0) = 1/3.
  • Step 7: Conclude that the value of the integral ∫(0 to 1) x^2 dx is 1/3.
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