What is the integral of x^2 with respect to x? (2021)

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Question: What is the integral of x^2 with respect to x? (2021)

Options:

Correct Answer: (1/3)x^3 + C

Solution:

The integral of x^n is (1/(n+1))x^(n+1) + C. Here, n=2, so the integral is (1/3)x^3 + C.

What is the integral of x^2 with respect to x? (2021)

What is the integral of x^2 with respect to x? (2021)

Step 1: Identify the function you want to integrate. In this case, it is x^2.
Step 2: Recognize that you will use the power rule for integration, which states that the integral of x^n is (1/(n+1))x^(n+1) + C.
Step 3: Determine the value of n. Here, n is 2 because we have x^2.
Step 4: Apply the power rule. Substitute n = 2 into the formula: (1/(2+1))x^(2+1) + C.
Step 5: Simplify the expression. This becomes (1/3)x^3 + C.
Step 6: Write down the final answer: The integral of x^2 with respect to x is (1/3)x^3 + C.

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