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Q6. The Stefan-Boltzmann constant (20 points) The Planck theory of thermal radiation tells us that in the angular frequency interval to + d, a black body of unit area radiates an amount of thermal energy per second equal to I()d, where I()=42c2(ekBT1)3 (ref. PHY3202 or PHY3251) Here is Planck's constant over 2,c is the speed of light, and kB is the Boltzmann's constant. The total energy per unit area per second radiated by a black body is W=42c23kB4T40ex1x3dx (Optional) Derive the equation for W above using the given I(). (a) Write a program to evaluate the integral in the expression of W. Explain what method you used, and how accurate you think your answer is. (b) Even before Planck gave his theory of thermal radiation around 20th century, it was known that the total energy W given off by a black body per unit area per second followed Stefan's law: W=T4, where is called the Stefan-Boltzmann constant. Use your result in (a), compute the value for (in SI units) to 3 significant figures. Compare your result to the known value, which you can find in books or on-line