Answer: π.
- A π
- B 2π
- C 0
- D π/2
Correct answer: A. π
Explanation: Integration by parts: u=x, dv=sinx dx → du=dx, v=−cosx. [−x cosx]₀^π + ∫₀^π cosx dx = (−π cosπ+0) + [sinx]₀^π = π + 0 = π.
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.