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6. Sketch then find the centroid of the region bounded by the curves y = sinx, y = 0, x = m/4 and x = 3n/4. 7. The demand function of a commodity is given by p = 40 - 0.1x - 0.01x2, x 2 0; and the supply function for that same commodity is given by Ps = 0.1x + 0.01x2, x 2 0. a. Find the market equilibrium Spro b. Compute the maximum total surplus for the commodity. 8. We consider the probability density function p(r) = 4re-2, r 2 0 where r is the distance from a fixed position. . Verify that p(r) is indeed a probability density function. Make sure you show your work. Spra b. Calculate the mean distance (from the fixed position)