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Problem 1. For the area bounded by the two curves, determine the following: a. Area b. First moment of the shaded area with respect to x-axis c. First moment of the shaded area with respect to y-axis 12

Problem 1. For the area bounded by the two curves, determine the following: a. Area b. First moment of the shaded area with respect to x-axis c. First moment of the shaded area with respect to y-axis 12

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Problem 1. For the area bounded by the two curves, determine the following: a. Area b. First moment of the shaded area with respect to x-axis c. First moment of the shaded area with respect to y-axis d. Centroid (x,y) e. Volume of the resulting solid, if the region bounded by the two curves is revolved about x = 4 f. Moment of inertia with respect to x and y axis All dimensions are in cm. 12 y = vx + vx? -1 3 y = ux? - vx - 3 Once the integrals have been set up, show the integrated form of the equation as part of your solution. For example: A = | (4x³ – 3x²)dx 2 A = (x* – x³)|£ A = 184 cm² Answers: A = 10.6667 cm², Qx = 12.8 cm?, Q, = 10.6667 cm³, (x,y) = (1,1.2), V=201.0626 cm³, k= 119.4667 cm*, = 19.6 cm4 %3D
Transcribed Image Text:Problem 1. For the area bounded by the two curves, determine the following: a. Area b. First moment of the shaded area with respect to x-axis c. First moment of the shaded area with respect to y-axis d. Centroid (x,y) e. Volume of the resulting solid, if the region bounded by the two curves is revolved about x = 4 f. Moment of inertia with respect to x and y axis All dimensions are in cm. 12 y = vx + vx? -1 3 y = ux? - vx - 3 Once the integrals have been set up, show the integrated form of the equation as part of your solution. For example: A = | (4x³ – 3x²)dx 2 A = (x* – x³)|£ A = 184 cm² Answers: A = 10.6667 cm², Qx = 12.8 cm?, Q, = 10.6667 cm³, (x,y) = (1,1.2), V=201.0626 cm³, k= 119.4667 cm*, = 19.6 cm4 %3D
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