Question: Evaluate the integral ∫ (3x^2 + 2x) dx. (2020)
Options:
x^3 + x^2 + C
x^3 + x^2 + 2C
x^3 + x^2 + 1
x^3 + 2x + C
Correct Answer: x^3 + x^2 + C
Solution:
The integral is (3/3)x^3 + (2/2)x^2 + C = x^3 + x^2 + C.
Evaluate the integral ∫ (3x^2 + 2x) dx. (2020)
Practice Questions
Q1
Evaluate the integral ∫ (3x^2 + 2x) dx. (2020)
x^3 + x^2 + C
x^3 + x^2 + 2C
x^3 + x^2 + 1
x^3 + 2x + C
Questions & Step-by-Step Solutions
Evaluate the integral ∫ (3x^2 + 2x) dx. (2020)
Step 1: Identify the integral you need to evaluate, which is ∫ (3x^2 + 2x) dx.
Step 2: Break down the integral into two parts: ∫ 3x^2 dx and ∫ 2x dx.
Step 3: For the first part, ∫ 3x^2 dx, use the power rule of integration. The power rule states that ∫ x^n dx = (1/(n+1))x^(n+1) + C. Here, n is 2, so you get (3/(2+1))x^(2+1) = (3/3)x^3 = x^3.
Step 4: For the second part, ∫ 2x dx, again use the power rule. Here, n is 1, so you get (2/(1+1))x^(1+1) = (2/2)x^2 = x^2.
Step 5: Combine the results from Step 3 and Step 4. You have x^3 + x^2.
Step 6: Don't forget to add the constant of integration, C, to your final answer.
Step 7: Write the final answer as x^3 + x^2 + C.
Integration of Polynomials – The process of finding the antiderivative of polynomial functions by applying the power rule.
Soulshift Feedback×
On a scale of 0–10, how likely are you to recommend
The Soulshift Academy?
