Quiz 4 Write and evaluate the integrals necessary to find the area between the graphs off and g for x in the given interval. 1. f[x) = cos[x), g[x) = sin[x), and 0 S x S 21: 2. f(x)=2,g(x)=\\/4x2and 2$x$2 3. Find the average value of f[x) = x2 on the interval [-3, 3] 4. Calculate the average value off(x) = x/E on the interval [0, C] for C = 1, 9, 81, 100 What is the pattern? 5. How much work is done lifting a 60-pound chair from the ground to the top ofa 20 foot building with a cable which weighs 3 pounds per foot? 6. How much work is done lifting a 160 pound injured adult to the top ofa 30 foot hole using a stretcher weighing 10 pounds and a cable which weighs 2 pounds per foot? 7. Consider the integral 2 x a) Find To b) Find S6 c) Calculate the exact value of the integral (You may need to use your calculator) 8. Represent the volume as an integral and evaluate the integral. circles y = Vx11. Find the volume swept out when the region between y = x2 and y = 6 - x for 2 s x - 5 is revolved about the line x = -1. 12. Find the volume when the region bounded by y = x2 and y = -2(x - 3)2 + 9 is revolved about the liney = -2