Which of the following integrals will find the area of the surface generated by revolving the curve f(x) = 4 cos(x) with 0 < x< about the х-ахis? a) O 8 n cos(x)\/1+ [4 cos(x)} dr a13 b) O 8n cos(x)\/1+[-4 sin(x)† dx z/3 c) O 4 a cos(x)\/1+[-4 sin(x)} dx

Q: 6. Let C be the positively oriented circle centered at the origin with radius Without evaluating the…

A: We will use the principal branch of logarithm

Q: Set up a (sum of) definite integral(s) that is equal to the arc length of the portion of the curve y…

A: The length of the curve y=f(x) between the limits x=a to x=b is given by; L=∫ab1+dydx2dx

Q: 6.4.12 Please help me solve these math practice questions.

A: Area of the curve y= cos(4x)  Where -π/8&lt;x&lt;π/8

Q: Write an integral for the area of the surface generated by revolving the curve y = cos(4x) about the…

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Q: Consider the arc L: y = 1+ cosa from (0, 2) to (,¹). of the surface formed when I is revolved about…

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Q: Use Green’s Theorem to evaluate  ∫ sin 5y dx + 5x dy  around the boundary curve C of the region R,…

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Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. 5y +…

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Q: 12. Consider the arc L : y = 1 + cos z from (0, 2) to (,1). Which of the following integrals give…

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Q: The given curve is rotated about the x-axis. Set up, but do not evaluate, an integral for the area…

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Q: Give an approximation of the following integrals using Composite Trapezoidal rule: a) os- cos(x) dr…

A: Trapezoidal rule ∫abf(x)dx≈Δx2​(f(x0​)+2f(x1​)+2f(x2​)+2f(x3​)+⋯+2f(xn−2​)+2f(xn−1​)+f(xn​)) where…

Q: The graphs of y = sin r and y = cos x are shown below. Set up an integral or sum of 9. %3D %3D…

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Q: Which integral computes arc length of f(x) = 5/2 on 0, 1 1 1+ x° dx 0. 1 I V1+x³ dx 0. 1 49 7 1+x'…

A: Given function: fx=x52 on interval [0,1] Differentiate the given function w.r.t "x"…

Q: use Green's Theorem to evaluate the line integral around the given closed curve. ∮C (3x + 5 y - cos…

A: Consider the given integral as ∮3x+5y-cosydx+xsinydy

Q: Find the surface area of the region that comes from rotating the given curve about the x-axis: T X =…

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Q: The integral dx is improper for two reasons: The interval [0, co) is infinite and the integrand has…

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Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. 5y +…

A: Use Green Theorem to evaluate  ∫C5y+9exdx+10x+7cosy2dy where, C is the boundary of the region…

Q: 12. Consider the arc L: y = 1+ cos z from (0,2) to (.1). Which of the following integrals give the…

A: Given arc  y=1+cosx From x=0 to x=π2

Q: 2. Set up a double integral using polar cor r=4sin 30. Do not evaluate. nates that will yield the…

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Q: 2. Let R be the region inside the curve C :r=1+ cos 0 and to the right of the line l :r = 3 sec 0.…

A: To find point of intersection equate both r and find value of  θ which lie in the interval -π,π For…

Q: Use Green's Theorem to compute the area of the plane region bounded by the x-axis and the arc of the…

A: x=2π-t+sint y=1-cost 0≤t≤2π

Q: The arc-length of the curve y= Vcos(4t) dt, for 0<x<; is given by which of the following 8…

A: We will use the formula for Length of the arc and fundamental theorem of Calculus.

Q: Which of the following integrals will find the area of the surface generated by revolving the curve…

A: fx=x3 is a polynomial function. It is continuous in the interval 0,3.

Q: 1. Find the area of surface that is generated by revolving the portion of the curve y = V4- r2…

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Q: Use Property 11 to estimate the integral xxD esin x cos y dA, where is thedisk with center the…

A: We know that –1 ≤ sin x ≤ 1 and –1 ≤ cos y ≤ 1, Hence, –1 ≤ sin x cos y ≤ 1

Q: 8) Let x= 2t - sin(2t) and y=- cos(2t). Set up an integral in parametric form to determine the…

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Q: Use Green's theorem to evaluate the line integral along the given positively oriented curve. | (3y +…

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Q: Over the region R={(x,y)|π6≤x≤π3,π6≤y≤π3}, we have 14≤cos(x)cos(y)≤34. Use this to find a lower…

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Q: Evaluate the line integral S¢F dr where F(x, y) = xsin(y)i + yj and C is the arc of the parabola…

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Q: Calculate the integral Sy3dx + (x3 + 3xyl)dy in the following ways; A) in shape direct. B) using…

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Q: Which of the following integrals represents the area of the surface obtained by rotating the curve y…

A: NOTE: Refresh your page if you can't see any equations. . take derivative the given interval is…

Q: Consider the following curve. y = x³, osxS 5 Set up an integral in terms of x that can be used to…

A: The surface area of revolution about the x-axis is: S=2π∫abf(x)1+f'(x)2dx If the function is,…

Q: Which of the following integrals represents the length of the parametric curve x =t+ cos(t), y =t -…

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Q: Consider the following curve. y = x, 0sxs 3 Set up an integral in terms of x that can be used to…

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Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. |(3y +…

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Q: у 3 1 + sin х, 0 <x< т/2 y

A: The given curve is y=1+sinx and the limit is 0≤x≤π2 The Surface area is given by S=∫x2πy1+y'2dx or…

Q: Suppose we want to find the area enclosed by the curves y1 (z) = sin(z) and y2(z) cos(z) %3D %3D to…

A: We will answer the first question since exact one was not specified. Please resubmit the question…

Q: Which integral expresses the arc length of y= In(cos x) from x = n / 6 to x = T |4? | sec(x) dx |…

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Q: Use the property to estimate the best possible bounds of the integral. II 4 sin*(x + y) dA, Tis the…

A: Consider the given integral: ∫∫T4sin4x+ydA T is a triangle enclosed by lines y =0, y = 2x and x =3.…

Q: The arc length along the parabola y = x² from (1,1) to (2,4) is given by which of the following…

A: Let's find.

Q: Express the area of the surface obtained by rotating the curve y =In sec(2x) between x = 0 and x =…

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Q: Set up and evaluate the definite integral for the area of the surface generated by revolving the…

A: y=16-x2,  -1≤x≤1 Differentiating with respect to x, we get…

Q: Which ONE of the following integrals correctly represents the area of the surface of revolution…

A: giveny=ln(x5)rotation about x-axisA=∫152πyds

Q: Calculate the area between the curves r2 16 sin 20 and p2 16 cos 20 .Show by drawing. %3D %3D

A: We will draw region first, then find the area using double integral

Q: cosz-sinz dz with C:|z|=2 using Cauchy's integral formula (zti) Evaluate '

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Q: Find the line integral of C in two ways; A) Directly. B) Using Green's theorem. C eata formed by the…

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Q: which of the following integrals represents the area of the surface obtained by rotating the curve…

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Q: If the curve y= from (0, 0) to (3,9) is rotated about the x-axis, the integral that represents the…

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Q: Jy Find the area of the inner loop of the curve r = 9 cos 0 - 4 by using double integral.

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Q: - SxS Write an integral for the area of the surface generated by revolving the curve y = cos (3x)…

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