(a) determine the average value of the following functions on the interval [1,2]. give your answers first in exact form, and then in decimal form with at least three decimal digits. y = x, average value = incorrect: your answer is incorrect. (exact)average value ≈ 0.0678 (decimal)y = x2, average value = (exact)average value ≈ (decimal)y = x3, average value = (exact)average value ≈ (decimal)y = x4, average value = (exact)average value ≈ (decimal)(b) determine the average value of the following functions on the interval [0,π/2]. give your answers first in exact form, and then in decimal form with at least three decimal digits. y = cos x, average value = (exact)average value ≈ (decimal)y = cos2 x, average value = (exact)average value ≈ (decimal)y = cos3 x, average value = (exact)average value ≈ (decimal)y = cos4 x, average value = (exact)average value ≈ (decimal)(c) the average values in part (a) increased, while the average values in part (b) decreased. the reason for this is thatthe interval [1,2] is shorter than the interval [0,π/2].each function in part (a) is an increasing function of x in [1,2], while each function in part (b) is a decreasing function of x in [0,π/2]. when y > 1, we have y < y2 < y3 < y4, while when 0 < y < 1, we have y > y2 > y3 > y4.