Riemann Sum Worksheet Attached, you will find three copies of the graph of f(z) = √4- (z-3)²- 1. Goal: approximate the a

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Riemann Sum Worksheet Attached, you will find three copies of the graph of f(z) = √4- (z-3)²- 1. Goal: approximate the area under the curve using four rectangles, using the right hand side of the rectangle to find the height. (ii) On your graph, 21 = (i) Sketch the four rectangles you will use on your graph. (Graphs provided on last page) Ig= I₁ = 4- Math& 152: Calculus II (ii) Height of rectangle 1 Height of rectangle 2 Height of rectangle 3 Height of rectangle 4 = f(₂)= = f(₂) = f(x) = f(x) (iii) The width of each rectangle is Ar = I
(iv) → Area of rectangle 1 Area of rectangle 2 Area of rectangle 3 Area of rectangle 4 = f(₁) Ar = f(x₂) Ar = f(a) Ar = f(x₁) Az → Total approximate area = 22 22 2 Σf(z.)Az i=1 +
2. Goal: Approximate the area under the curve using 16 rectangles and right-hand Rie- mann sums, using # 1 as a guide. 3
3. Imagine doing this with 1000 rectangles. Draw "1000" rectangles on a graph. What do you notice? 4. Using geometry, find the exact area under the curve.