The area under a sine wave refers to the total space enclosed by the curve of a sine function and the x-axis. It represents the total displacement of the wave over a given interval.
The function of -cosx represents the derivative of the sine function. Taking the anti-derivative of -cosx will give us the original function, which is the sine wave. Therefore, the area under the sine wave can be determined by taking the anti-derivative of -cosx.
The area under a sine wave has many applications in mathematics and science. It is used in calculating the displacement, velocity, and acceleration of objects in simple harmonic motion. It is also used in calculating the total energy and power of oscillating systems.
To calculate the area under a sine wave, you can use integration techniques. First, determine the limits of integration, which are the starting and ending points of the interval. Then, take the anti-derivative of -cosx, which is sinx, and evaluate it at the limits of integration. Finally, subtract the lower limit from the upper limit to get the area under the curve.
No, the area under a sine wave can be positive or negative, depending on the limits of integration. If the limits are both positive or both negative, then the area will be positive. However, if the limits are on opposite sides of the x-axis, then the area will be negative.