Source: Extra Practice
The area bounded by the curve y = cos x, x-axis and the lines x = 0 and x = π is:
Options
Option A
1 sq. unit
Option B is correct
2 sq. units
Option C
0 sq. units
Option D
π sq. units
Explanation
Area = ∫[0 to π/2] cos x dx + |∫[π/2 to π] cos x dx|. This is because cos x is positive in [0, π/2] and negative in [π/2, π]. Area = [sin x] from 0 to π/2 + |[sin x] from π/2 to π| = (1 - 0) + |0 - 1| = 1 + 1 = 2. Option C is the value of the definite integral, not the physical area. Option A and D are incorrect.