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candice_84 said:
No solid angle is the solid angle, like angle is angle in 2D. The 4π (steradians) solid angle is the 3D analog to 2π radians in 2D.candice_84 said:
Integration over 4π refers to the process of summing up or calculating the area under a curve that extends over 4π units on the x-axis. This is typically done in calculus or physics to find the total value of a function over a specific range.
Integrating over 4π allows us to find the total value of a function over a larger range than just 2π, which is the standard range for trigonometric functions. This can be useful in various applications, such as calculating the total displacement or velocity of an object in circular motion.
The number 4π represents the circumference of a full circle in radians, which is equivalent to 360 degrees. By integrating over this range, we are essentially calculating the value of a function over a complete rotation, which can have practical applications in physics and engineering.
The need to integrate over 4π depends on the specific problem at hand. In some cases, integrating over 2π may be sufficient, but there are situations where a larger range is necessary to accurately represent the behavior of a function. It is important to carefully consider the problem and choose the appropriate integration range.
Integrating over 4π covers a larger range and allows for a more comprehensive calculation of a function's total value. Integrating over 2π is typically used for trigonometric functions and represents one full cycle. In some cases, integrating over 4π may yield a different result than integrating over 2π, depending on the behavior of the function.
