Final answer:
The area under one arch of the curve y = sin(x) from x = 0 to x = π is calculated using integration and is equal to 2 square units.
Step-by-step explanation:
To find the area (A) under one arch of the curve y = sin(x), we need to consider the integral of the sine function over one period. A single arch, or period, of the sine wave, is between x = 0 and x = π because sin(x) completes a full cycle back to its starting value over this interval. We calculate the area under the curve by integrating the sine function within these limits.
The integral of sin(x) from 0 to π is as follows:
- Set up the integral: ∫ sin(x) dx from x=0 to x=π.
- Compute the integral: -cos(x) from x=0 to x=π.
- Apply the Fundamental Theorem of Calculus: (-cos(π) - (-cos(0)) = (1 - (-1)) = 2.
Therefore, the area under one arch of the sine curve is 2 square units.