7-9 Evaluate the double
8.
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Essential Calculus: Early Transcendentals
- A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in inches. a. Using the fact that the volume of the can is 25 cubic inches, express h in terms of x. b. Express the total surface area S of the can in terms of x.arrow_forward11. Evaluate the double integral , (1-x)dA where R = [0, 1] x [0.2] by first identifying it as the volume %3D | of the solid. Sketch the solid.arrow_forward(e^(x-2y))/4 below by xy plane for x is less than or equal to 0 and y is greater than or equal to 0. Create a double integral to represent the volume, and find the volume.arrow_forward
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- I found a textbook example which intergrates an area function to find the volume of a solid of revolution bounded by the curve f(x) = (x-1)2 about the x-axis and the lines x=0 and x=2 using the disk method. The example shows a final solution change of intergration interval to x=1 and x=3 to arrive at the answer of 242pi/3 instead of the original interval x=0 and x=2? Would you show me step-wise how this was done or why it was necessary?arrow_forwardConsider the region bounded by the graphs of y = ln 2x, y = ex , x = 1/2, and x = pi. Set up a definite integral to find the volume of the solid that is formed by revolving the region abouta. the x- axis b. the line x=-1/2arrow_forward4. Evaluate the double integral over rectangle S, xycosy dA, R:[-1,2] x [0, Pi]arrow_forward
- Find constant K, K positive, so that the volume of the solid of revolution determined by rotating the area bounded by f(x) = x2 and g(x) = - x(x - K) is equal to 200 Pi.arrow_forwardConsider the region bounded by the graphs of y = ln 3x, y = 2ex , x = pi, and x = 1/2. Set up a definite integral to find the volume of the solid that is formed by revolving the region abouta. the y-axis b. the line y=-1/2arrow_forward18. Using the triple integral find the volume of the region cut from the cylinder x2 + y2 = 4 by the planes z = 0 and x+z= 3. Set up the iterated integral but do not evaluate it.arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning