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

Practice Questions

Q1
What is the value of the integral ∫(1 to 2) (3x^2 - 2)dx?
  1. 3
  2. 4
  3. 5
  4. 6

Questions & Step-by-Step Solutions

What is the value of the integral ∫(1 to 2) (3x^2 - 2)dx?
  • Step 1: Identify the integral you need to solve: ∫(1 to 2) (3x^2 - 2)dx.
  • Step 2: Find the antiderivative of the function 3x^2 - 2. The antiderivative is x^3 - 2x.
  • Step 3: Evaluate the antiderivative at the upper limit (2): Substitute x = 2 into x^3 - 2x, which gives 2^3 - 2*2 = 8 - 4 = 4.
  • Step 4: Evaluate the antiderivative at the lower limit (1): Substitute x = 1 into x^3 - 2x, which gives 1^3 - 2*1 = 1 - 2 = -1.
  • Step 5: Subtract the value at the lower limit from the value at the upper limit: 4 - (-1) = 4 + 1 = 5.
  • Step 6: The final answer is 5.
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