Question

Evaluate \( \int_{0}^{1} (2x + 1) \, dx \).

• A. \( 1 \)
• B. \( 2 \)
• C. \( 3 \)
• D. \( 4 \)

Hint:

To evaluate a definite integral, find the antiderivative, apply the limits, and compute the difference: \( F(b) - F(a) \).

Answer 1

The Correct Option is B

To evaluate the integral \( \int_{0}^{1} (2x + 1) \, dx \), find the antiderivative of \( 2x + 1 \): \[ \int (2x + 1) \, dx = \int 2x \, dx + \int 1 \, dx = x^2 + x + C \] Apply the limits from 0 to 1: \[ \left[ x^2 + x \right]_{0}^{1} = (1^2 + 1) - (0^2 + 0) = 1 + 1 - 0 = 2 \] Thus, the value of the integral is: \[ {2} \]