1)Consider the expression for blackbody radiation given by Equation 4.62 . The integral of this expression over all wavelengths, that is, , gives the total energy radiated by a blackbody per unit area and time. Using Simpson’s rule, compute this integral at T=1000K as accurately as possible. The analytical result is given in the literature as , where is known as the Stehan-Boltzman constant and has a value of 5.67×10^(-8) W/m^2K^4. Compare your numerical result with the analytical value at 1000K. Equation 4.62 is also attached as an image.
2)The RMS value of an electric current I(t), where I varies periodically with time t is given by the expression where is the time period for one cycle in the variation of I(t). If I(t) is given as 5e^(-t)sin4pit, with =0.5 seconds, compute the RMS value using Simpson’s Rule.
3)The fluid velocity V is measured at several radial locations r for flow in a circular pipe of radius 1 cm. The velocities in cm/s are tabulated as follows
r(cm)
0
0.2
0.5
0.6
0.8
0.9
1.0
V(cm/s)
1.0
0.96
0.75
0.64
0.36
0.19
0.0
The volume flow in the pipe is given by the integral , where R is the radius of the pipe. Using the data given, compute the integral.
4)Using Simpson’s rule, compute the improper integral as accurately as possible.
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