18. Find the average value of the function f(x) = (-1, 1]. on (13 + 3)
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![17. The base of S is the triangular region with vertices (0, 0), (1,0), and (0, 1). Cross-sections
perpendicular to the x-axis are squares.
18. Find the average value of the function f(r) =
on [–1, 1].
2
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- Suppose that X and Y are independent measurement of a quantity μ. E(X) = E(Y) = μ, σX ≠ σY, Z = αX + (1 - α)Y, α ∈ [0, 1] (a) Show that E(X) = μ. (b) Find α in terms of σX and σY to minimize V(Z). (c) Under what circumstance is it better to use the average (X+Y)/2 than either X or Y alone?Find the average value of the function on the giveninterval. f(x) = x -x2, [0,2]Compute the average value of the function f(x) = (8x^2+8x+20)e^x on the interval [−8, 8]
- 12) Find the clamped cubic spline for the data (1.1).(3,4), using that f'(1) - 2.f(3) = 5I would appreciate someone helping me with this problem . Let T to the trapezoid bounded by the graphs of y = x, y = 2x, x = 1, and x = 2. Find the average value of f(x, y) = y / (x2 + y2) over T.1. Estimate the volume of the solid that lies below the surface z = xy and above the rectangle R = {(x,y) | 0 ≤ x ≤ 6, 0 ≤ y ≤ 4}.(a) using Riemann sum with m = 3, n = 2, and take the sample point to be the upper the right corner of each square(b) using midpoint rule with the same values of m and n in problem (a).