Answer: ln|x³ + x²| + C.
- A ln|x³ + x²| + C
- B ln|x| + C
- C ln|x + 1| + C
- D 3 + C
Correct answer: A. ln|x³ + x²| + C
Explanation: Numerator is derivative of denominator: d/dx(x³+x²) = 3x²+2x. So integral = ln|x³+x²| + 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.