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

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

Options:

Correct Answer: x^3 + C

Exam Year: 2021

Solution:

The integral of 3x^2 is (3/3)x^3 + C = x^3 + C.

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

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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