Answer: eˣ(x-1) + C.
- A x eˣ + eˣ + C
- B eˣ(x-1) + C
- C x eˣ - eˣ + C
- D x eˣ + C
Correct answer: B. eˣ(x-1) + C
Explanation: By parts: u=x, dv=eˣdx. uv - integral(v du) = x eˣ - integral(eˣ dx) = x eˣ - eˣ + C = eˣ(x-1) + 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.