A rectangular lake is 140 km long and 3 km wide. The vertical cross- section through...

 
 

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A rectangular lake is 140 km long and 3 km wide. The vertical cross- section through the lake in the figure below shows that the lake is 0.2 km deep at the center. Set up and evaluate a definite integral giving the total volume of water in the lake. Slice perpendicularly to either the height, width, or length. Call the depth h, the width w, and the length 1. 3 km 1 0.2 km The definite integral describing the total volume over all slices is (a) Find an expression for the area of the shaded strip in the figure as it would appear in a Riemann sum. Area of strip (y- y²) dy (b) Write a definite integral to represent the total area of the region. X Ay y = x Т A rectangular lake is 140 km long and 3 km wide. The vertical cross- section through the lake in the figure below shows that the lake is 0.2 km deep at the center. Set up and evaluate a definite integral giving the total volume of water in the lake. Slice perpendicularly to either the height, width, or length. Call the depth h, the width w, and the length 1. 3 km 1 0.2 km The definite integral describing the total volume over all slices is (a) Find an expression for the area of the shaded strip in the figure as it would appear in a Riemann sum. Area of strip (y- y²) dy (b) Write a definite integral to represent the total area of the region. X Ay y = x Т

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Given Data The length of the lake is 1 140 km The width is b 3 km The dep... View the full answer