Find ∫ (6x^5) dx. (2022)

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Question: Find ∫ (6x^5) dx. (2022)

Options:

Correct Answer: x^6 + C

Exam Year: 2022

Solution:

The integral is (6/6)x^6 + C = x^6 + C.

Find ∫ (6x^5) dx. (2022)

Find ∫ (6x^5) dx. (2022)

Step 1: Identify the function to integrate, which is 6x^5.
Step 2: Use the power rule for integration. The power rule states that ∫x^n dx = (1/(n+1))x^(n+1) + C, where n is the exponent.
Step 3: In our case, n is 5. So, we apply the power rule: ∫(6x^5) dx = 6 * (1/(5+1))x^(5+1) + C.
Step 4: Calculate (5+1) which equals 6. Now we have: ∫(6x^5) dx = 6 * (1/6)x^6 + C.
Step 5: Simplify the expression: 6 * (1/6) equals 1, so we get x^6 + C.
Step 6: Write the final answer: ∫(6x^5) dx = x^6 + C.

Integration of Polynomials – The question tests the ability to integrate a polynomial function using the power rule.