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What is the integral of the function f(x) = 3x^2? (2021)

Practice Questions

Q1
What is the integral of the function f(x) = 3x^2? (2021)
  1. x^3 + C
  2. x^3 + 3C
  3. x^3 + 1
  4. 3x^3 + C

Questions & Step-by-Step Solutions

What is the integral of the function f(x) = 3x^2? (2021)
  • Step 1: Identify the function you want to integrate, which is f(x) = 3x^2.
  • Step 2: Recall the power rule for integration, which states that the integral of x^n is (1/(n+1))x^(n+1) + C, where C is the constant of integration.
  • Step 3: In our case, n is 2 because we have x^2. So, we will apply the power rule.
  • Step 4: Add 1 to the exponent: 2 + 1 = 3.
  • Step 5: Divide the coefficient (3) by the new exponent (3): (3/3) = 1.
  • Step 6: Write the result as x^3 + C, where C is the constant of integration.
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