Question: What is the integral of x^3 + 2x? (2021)
Options:
(1/4)x^4 + x^2 + C
(1/3)x^3 + x^2 + C
(1/4)x^4 + (1/2)x^2 + C
(1/5)x^5 + (1/2)x^2 + C
Correct Answer: (1/4)x^4 + (1/2)x^2 + C
Exam Year: 2021
Solution:
Integrating term by term, ∫x^3dx = (1/4)x^4 and ∫2xdx = x^2. Thus, ∫(x^3 + 2x)dx = (1/4)x^4 + (1/2)x^2 + C.
What is the integral of x^3 + 2x? (2021)
Practice Questions
Q1
What is the integral of x^3 + 2x? (2021)
(1/4)x^4 + x^2 + C
(1/3)x^3 + x^2 + C
(1/4)x^4 + (1/2)x^2 + C
(1/5)x^5 + (1/2)x^2 + C
Questions & Step-by-Step Solutions
What is the integral of x^3 + 2x? (2021)
Step 1: Identify the function to integrate, which is x^3 + 2x.
Step 2: Break the integral into two parts: ∫(x^3 + 2x)dx = ∫x^3dx + ∫2xdx.
Step 3: Integrate the first part, ∫x^3dx. Use the power rule: add 1 to the exponent (3 + 1 = 4) and divide by the new exponent. This gives (1/4)x^4.
Step 4: Integrate the second part, ∫2xdx. Again, use the power rule: add 1 to the exponent (1 + 1 = 2) and divide by the new exponent. This gives (2/2)x^2, which simplifies to x^2.
Step 5: Combine the results from Step 3 and Step 4. You get (1/4)x^4 + x^2.
Step 6: Don't forget to add the constant of integration, C. So the final answer is (1/4)x^4 + x^2 + C.
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