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

Practice Questions

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

Questions & Step-by-Step Solutions

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