Answer: (1/a)tan⁻¹(x/a) + C.
- A (1/a)tan⁻¹(x/a) + C
- B tan⁻¹(x/a) + C
- C (1/a)tan⁻¹(x) + C
- D (1/a²)tan⁻¹(x/a) + C
Correct answer: A. (1/a)tan⁻¹(x/a) + C
Explanation: Standard result: integral of 1/(x²+a²) dx = (1/a)tan⁻¹(x/a) + 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.