Answer: x²/2 × ln x - x²/4 + C.
- A x²/2 × ln x - x²/4 + C
- B x²lnx + C
- C ln x + C
- D x² ln x + x² + C
Correct answer: A. x²/2 × ln x - x²/4 + C
Explanation: u = lnx, dv = x dx. v = x²/2. uv - integral(v du) = (x²/2)lnx - integral(x²/2 × 1/x dx) = (x²/2)lnx - x²/4 + 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.