Evaluate the integral ∫(2x + 3) dx. (2021)

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Question: Evaluate the integral ∫(2x + 3) dx. (2021)

Options:

Correct Answer: x^2 + 3x + C

Exam Year: 2021

Solution:

The integral of (2x + 3) is (2x^2/2) + 3x + C = x^2 + 3x + C.

Evaluate the integral ∫(2x + 3) dx. (2021)

Evaluate the integral ∫(2x + 3) dx. (2021)

Step 1: Identify the function to integrate, which is (2x + 3).
Step 2: Break down the integral into two parts: ∫(2x) dx and ∫(3) dx.
Step 3: For the first part, ∫(2x) dx, use the power rule: increase the exponent of x by 1 (from 1 to 2) and divide by the new exponent. This gives (2x^2/2).
Step 4: Simplify (2x^2/2) to x^2.
Step 5: For the second part, ∫(3) dx, since 3 is a constant, multiply it by x. This gives 3x.
Step 6: Combine the results from Step 4 and Step 5. You get x^2 + 3x.
Step 7: Add the constant of integration, C, to the result. The final answer is x^2 + 3x + C.

Integration of Polynomials – The question tests the ability to integrate a polynomial function, specifically applying the power rule for integration.