Source: Extra Practice
The area bounded by the curve y = sin x between x = 0 and x = π is:
Options
Option A
0 sq. units
Option B
1 sq. unit
Option C is correct
2 sq. units
Option D
4 sq. units
Explanation
Area = ∫[0 to π] sin x dx. The integral of sin x is -cos x. Area = [-cos x] from 0 to π = -cos(π) - (-cos(0)) = -(-1) + 1 = 1 + 1 = 2. Option A is the result of the integral of sin x from 0 to 2π (where signed area cancels), but from 0 to π, the area is positive. Options B and D are numerical mistakes.