Answer: (1/2)arctan(x/2) + C.
- A arctan(x/2) + C
- B (1/2)arctan(x/2) + C
- C (1/4)arctan(x/2) + C
- D (1/2)ln(x² + 4) + C
Correct answer: B. (1/2)arctan(x/2) + C
Explanation: ∫ dx/(x² + a²) = (1/a)arctan(x/a) + C; with a = 2 this is (1/2)arctan(x/2) + C.
The exact area under the curve from a to b (shaded) is approximated by a few rectangles, the Riemann sum idea behind the definite integral.