Evaluate the following integral:
${\int }_1^4(2x+1)dx$

• A. 16
• B. 24
• C. 12
• D. 18

Answer: (D)

Verified step by step guidance

1. Step 1: Identify the integral to be evaluated, which is ∫ from 1 to 4 of (2x + 1) dx.
2. Step 2: Apply the power rule for integration. The integral of 2x is x^2, and the integral of 1 is x. Therefore, the antiderivative of (2x + 1) is x^2 + x.
3. Step 3: Evaluate the antiderivative at the upper limit of integration, which is 4. Substitute x = 4 into the antiderivative to get 4^2 + 4.
4. Step 4: Evaluate the antiderivative at the lower limit of integration, which is 1. Substitute x = 1 into the antiderivative to get 1^2 + 1.
5. Step 5: Subtract the value obtained in Step 4 from the value obtained in Step 3 to find the definite integral. This will give you the final result.