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Evaluate the definite integral ∫(0 to 1) (3x^2)dx.

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Question: Evaluate the definite integral ∫(0 to 1) (3x^2)dx.

Options:

  1. 1
  2. 0.5
  3. 0.33
  4. 0.25

Correct Answer: 1

Solution: 

The integral evaluates to 1.

Evaluate the definite integral ∫(0 to 1) (3x^2)dx.

Practice Questions

Q1
Evaluate the definite integral ∫(0 to 1) (3x^2)dx.
  1. 1
  2. 0.5
  3. 0.33
  4. 0.25

Questions & Step-by-Step Solutions

Evaluate the definite integral ∫(0 to 1) (3x^2)dx.
  • Step 1: Identify the function to integrate, which is 3x^2.
  • Step 2: Find the antiderivative of 3x^2. The antiderivative is x^3.
  • Step 3: Evaluate the antiderivative at the upper limit (1) and lower limit (0).
  • Step 4: Calculate the value at the upper limit: (1)^3 = 1.
  • Step 5: Calculate the value at the lower limit: (0)^3 = 0.
  • Step 6: Subtract the lower limit value from the upper limit value: 1 - 0 = 1.
  • Definite Integral – The process of calculating the area under a curve defined by a function over a specified interval.
  • Power Rule of Integration – A method used to integrate polynomial functions, where the integral of x^n is (x^(n+1))/(n+1) + C.
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