Find ∫ (5x^4) dx. (2020)

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Question: Find ∫ (5x^4) dx. (2020)

Options:

Correct Answer: x^5 + C

Solution:

The integral is (5/5)x^5 + C = x^5 + C.

Find ∫ (5x^4) dx. (2020)

Find ∫ (5x^4) dx. (2020)

Step 1: Identify the function to integrate, which is 5x^4.
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 4. So, we apply the power rule: ∫x^4 dx = (1/(4+1))x^(4+1) + C.
Step 4: Calculate (1/5)x^5 + C, which simplifies to (1/5)x^5 + C.
Step 5: Now, multiply by the constant 5 from the original integral: 5 * ((1/5)x^5 + C) = x^5 + C.
Step 6: Write the final answer: ∫ (5x^4) dx = x^5 + C.

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