Accumulation/Area & Volume

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Accumulation/Area & Volume Alyssa, Camryn, Preetam

Class Work/Homework Classwork: Area & Volume MC: All FRQ: 11 Accumulations FRQ: 11 & 12 Homework: Area & Volume FRQ: 8 - 10 Accumulations FRQ: 9, 10, 13

Card 42: Riemann Sums (Left, Right, Midpoint) and Trapezoidal Approximation Method Δxn represents the sub-interval widths... Left: f(x0)Δx1 + f(x1)Δx2 + … + f(xn - 1)Δxn (using value of f at the left endpoint) *tangent line is under approximation for increasing function Right: f(x0)Δx1 + f(x1)Δx2 + … + f(xn - 1)Δxn (using value of f at the right endpoint) *tangent line is over approximation for increasing function Midpoint: f((x0 + x1)/2)Δx1 + f((x1 + x2)/2)Δx2 + … + f((xn - 1 + xn)/2)Δxn Trapezoidal: ½ [(f(x) + f(x))(Δx1) + (f(x) + f(x))(Δx1)] + … + ½ [(f(x) + f(x))(Δx1)]

Riemann Sum Graphs

Card 43: Area Between Curves When a and b are x-values, use the top function minus the bottom function When a and b are y-values, use the right function minus the left function

Card 44: Volume with Disk/Washer Method Disk Method Washer Method If the function is rotated around a horizontal line, use x-values for a and b, and make sure the functions are in terms of x If the function is rotated around a vertical line, use y-values for a and b, and make sure the functions are in terms of y When a and b are x-values, use the top function minus the bottom function When a and b are y-values, use the right function minus the left function

Card 45: Volume with Cross-Sections These formulas are in terms of a function perpendicular to the x-axis, if the function is perpendicular to the y-axis, use (right - left) If perpendicular to the x-axis use dx (a and b should be x-values, and the top and bottom functions should be in terms of x) IIf perpendicular to the y-axis use dy (a and b should be y-values, and the right and left functions should be in terms of y)

Card 46: Arc Length (Rectangular)