The phrase "integrating x * (cos x)^n between pi/2 and 0" refers to finding the definite integral of the function x * (cos x)^n from the upper limit of pi/2 to the lower limit of 0. This involves calculating the area under the curve of the function within the specified interval.
The purpose of integrating x * (cos x)^n between pi/2 and 0 is to evaluate the total value of the function within the given interval. This can be useful in various applications, such as calculating work done or determining average values.
The definite integral of x * (cos x)^n between pi/2 and 0 can be calculated using integration techniques such as substitution, integration by parts, or trigonometric identities. The specific method used will depend on the complexity of the function and the desired level of accuracy.
The limits pi/2 and 0 represent the upper and lower bounds of the interval over which the function is being integrated. In this case, the integration is being performed over the interval where cos x is positive, which is from pi/2 to 0. This choice of limits ensures that the function is continuous and well-defined within the interval.
The integral of x * (cos x)^n between pi/2 and 0 can be applied in fields such as physics and engineering to calculate the work done by a varying force or the average value of a periodic function. It can also be used in economics and finance to determine the net present value of investments with changing returns over time.