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5.4 Lab- Working with Integrals Student: Calculus I Determine if the integrand is even or odd. Then, use symmetry to evaluate the following denite integrals. 10 :12 1.) dz 1.) 1n V 200 $2 2.) f: cos(x)sin{z)d1: 2.) 2 3.) f (325~2)dz 3.) 72 Find the average value of the following functions on the given interval. 4.) f(1') : 12 + 1, [ - 2. 3] 4.) 5.) f(z) = sin(2:z}, [0, E] 5.) 6.) The surface ofa water wave is described by y = 5[1 + 1203(1)], 6.) for 11' S :1: 5 1r, where y = 0 corresponds to the trough of the wave. Find the average height of the wave above the trough on [ 7r, 7r]