Question 3Which of the following represents the volume of the solid generated by revolving the region bounded byf(x)=(x-1)³ and g(x)=x-1 about the x-axis?A1 [(x - 1) - (x - 1)²]dx - ₁ ² [(x - 1)²-(x - 1)]dxπ<- TB2mx[(x-1) - (x - 1)³]dx + 2x²x[(x-1)³- (x-1)]dx© 2n2x ["'x[(x− 1)³= (x− 1) ]dx + 2x ſªx[(x− 1) — (x− 1) ¹]dx-112Ⓒ π √ ²[XxDTS" [(x − 1)² = (x − 1)º]dx + ₁ [[(x - 1)²-(x - 1)]dx

Here we have to find the integral for finding the volume.

Answered: Which of the following represents the…

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 7 The volume of the solid obtained by rotating the region enclosed by y=1/(x^5), y=0, x=1, x=5 about the line x=-3 can be computed using the method of cylindrical shells via an integral V=∫__________________ dx (with lower limit of a and upper limit of b) with limits of integration a=_____________ and b=______________ The volume is V=_________________cubic units
Problem 8 The volume of the solid obtained by rotating the region enclosed by y=(e^3x)+3, y=0, x=0, x=0.2 about the x-axis can be computed using the method of disksor washers via an integral V=∫[upper limit=b, lower limit=a]______ dx with limits of integration a=______ and b=_______
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 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 4 The volume of the solid obtained by rotating the region enclosed by y=1/(x^3), y=0, x=2, x=7 about the y-axis can be computed using the method of cylindrical shells via an integral V=∫___________ dx (with lower limit a and upper limit b) with limits of integration a=_________ and b=__________ the volume is V= _______________ cubic units
- Find by integration the area of the triangle having vertices at (5, 1), (1, 3), and (-1,-2). - Find by integration the area of the triangle having vertices at (3, 4), (2, 0), and (0, 1). - Find the area of the region bounded by the curve x³ x² + 2xy - y² = 0 and the line x = 4. (HINT: Solve the cubic equation for y in terms of x, and express y as two functions of x.) Find the area of the region bounded by the three curves y = x², x = y³, and x + y = 2. Find the area of the region bounded by the three curves y = x², y = 8 - x², and 4x - y + 12 = 0.
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=__________
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
11. (A6-4) Find the centroid for the region bounded by the curve y = 4x − x^3 and the part of the x-axis on the interval [0, 2].
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=__________
Find the solution of the differential equation that satisfies the given boundary condition(s) . f" - 2f ' +5f= 0, f(0) = 1, f(π/4) = 0
Problem 12 The volume of the solid obtained by rotating the region enclosed by x=3y, y^3= x (with y>/=0) about the y-axis 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=_______

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