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Find ∫ (5x^4) dx. (2020)

Practice Questions

Q1
Find ∫ (5x^4) dx. (2020)
  1. x^5 + C
  2. x^5 + 5C
  3. x^5 + 1
  4. 5x^5 + C

Questions & Step-by-Step Solutions

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.
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