12.1 12.2: Problem 53Consider the integralf(x, y)dydx. Sketch the region3xof integration and change the order of integration.9.* 92(y)91(y)aa =gi (y) =[ 92(3)g2(y)

Answered: Image /qna-images/answer/1ba794f6-0b7c-4fcc-b009-b1c04300d175.jpg

Answered: 1 3 he integral I | f(x, y)dydx. 3x on…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Problem 10 The volume of the solid obtained by rotating the region bounded by y=(x^2), y=3x about the line y=9 can be computed using cylindrical shells via an integral V=∫_______________dy (with lower limit of alpha and upper limit of beta) with limits of integration alpha=_________ and beta=__________
Problem 11 The volume of the solid obtained by rotating the region bounded by y=(x^2), y=4x, about the line x=4 can be computed using the method of washers via an integral V=∫________________dy (with lower limit of a and upper limit of b) with limits of integration a=_________ and b=_________ The volume of this solid can also be computed using cylindrical shells via an integral V=∫_______________dx (with lower limt of alpha and upper limit of beta) with limits of integration alpha=_________ and beta=__________ In either case, the volume is V=______________ cubic units
Problem 12 The volume of the solid obtained by rotating the region bounded by y=(x^2), y=5x about the line x=-2 can be computed using the method of washers or disks via an integral V=∫________________dy (with lower limit of a and upper limit of b) with limits of integration a=_________ and b=_________ The volume of this solid can also be computed using cylindrical shells via an integral V=∫_______________dx (with lower limt of alpha and upper limit of beta) with limits of integration alpha=_________ and beta=__________ In either case, the volume is V=______________ cubic units
Problem 10 The volume of the solid obtained by rotating the region bounded by y=(x^2), y=3x about the line y=9 can be computed using the method of washers or disks via an integral V=∫________________dx (with lower limit of a and upper limit of b) with limits of integration a=_________ and b=_________ The volume of this solid can also be computed using cylindrical shells via an integral V=∫_______________dy (with lower limit of alpha and upper limit of beta) with limits of integration alpha=_________ and beta=__________
Problem 13 The volume of the solid obtained by rotating the region bounded by x=(y^2), x=5y about the line y=5 can be computed using the method of washers or disks via an integral V=∫________________dx (with lower limit of a and upper limit of b) with limits of integration a=_________ and b=_________ The volume of this solid can also be computed using cylindrical shells via an integral V=∫_______________dy (with lower limt of alpha and upper limit of beta) with limits of integration alpha=_________ and beta=__________
1.) Determine the Region in the xy plane for the differential equation dy/dx = cuberoot(xy) would have a unique solution that passes trhough (X0, Y0). b.) Is there a guaranteed unique solution to the differential equation that passes through (0,3).
Problem 9 The volume of the solid obtained by rotating the region bounded by x=(9y^2), y=1, x=0 about the y-axis can be computed using the method of washers or disks via an integral V=∫________________dy (with lower limit of a and upper limit of b) with limits of integration a=_________ and b=_________ The volume of this solid can also be computed using cylindrical shells via an integral V=∫_______________dx (with lower limt of alpha and upper limit of beta) with limits of integration alpha=_________ and beta=__________ In either case, the volume is V=______________ cubic units
Problem 11 The volume of the solid obtained by rotating the region enclosed by y=(x^2), y=6x, about the line x=0 can be computed using the method of disks or washers via an integral V=∫[upper limit=b, lower limit=a]________dy with limits of integration a=_______ and b=________
Suppose that X ∼ N(0,1). Compute E[X^2],E[X^3] and E[X^k]. (Hint: integration by parts may be useful)
Problem no.4: Use Simpson rule’ 1/3 Method with (n = 10) to estimate the y-integration function below: 10 y=|[ 1@ .ax 0 =0 0

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1 3 he integral I | f(x, y)dydx. 3x on and change the order of integra