Evaluate fpxV47x² + 47y² dA, where D is the shaded region enclosed by the lemniscate curve r? = sin(20) in the figure. r2= sin 20 0.5 0.5

Q: Find the area inside the curve r = 6 cos 20 and outside the curve: r = V3

A:

Q: Use the trapezoidal rule with n = 4 to approximate cos(x) dx finel

A:

Q: Find the arclength of the curve z 9 cos(9t), y = 9 sin(9t) with 0 <t< 36

A:

Q: 3. What is the length of the curve r = cos3 (-) where 0 < 0 <: sos

A: See the attachment

Q: Find the area between the inner and outer ovals of the curve r2 = 16(2 – cos 0)

A: Given,

Q: Find the points on the cardioid r = 1−cosθ at which there is a horizontal tangent line, a vertical…

A: Consider the given: r=1−cosθWrite the cartesian…

Q: Find fe F dr for F = 7yi - (sin y)j on the curve counterclockwise around the unit circle C starting…

A:

Q: Find the length L of the curve R(t) = e* cos(3t) i + e* sin(3t) j + 3e*k over the interval [1, 5]. L…

A: given: Rt=etcos3ti+etsin3tj+3etk interval 1,5

Q: Find the area between a large loop and the enclosed small loop of the curve  r = 4 + 8 cos(3θ).

A:

Q: Find the EXACT area inside the closed loop produced from the following parametric curve. Show ALL…

A: The area is the amount of space occupied by a two-dimensional figure. In other words, it is the…

Q: 1. Find the area of the region enclosed by loop of the curve T = cos(46 one 1.0 y

A:

Q: 24. Evaluate | x/x² + y² dA, where D is the shaded region enclosed by the lemniscate curve r² = sin…

A: Consider the given:

Q: Find the area of the region that lies inside the curve r = 2 + cos (2a), but outside the curve r = 2…

A: The given curves are r = 2 + cos (2a), r = 2 + sin(a). Use online graphing calculator and sketch the…

Q: Find the gardientoff at the indicatedpoint. frx,y)=D5sin x+Cos3y ;

A: Given: f(x,y)=5sinx2+cos3yπ2,0

Q: 2. Find the length of the curve 0<t< 2n. r(t) e'i + e' sin 2tj + e' cos 2tk,

A: From the given problem :   rt=eti+etsin2tj+etcos2tk   So,   x=et, y=etsin2t , z=etcos2t .   As we…

Q: Find the area between the inner and outer ovals of the curve r2 16(2 – cos 0)

A: To find the area between the inner and outer ovals of the curve

Q: Consider a particle moving along a path C given by r(t) = v3ti+ = V3ti sin (t)j + cos (t)k Find the…

A:

Q: Find the area of the region that lies inside r = 2 + cos 2θ but outside the curve r = 2 + sin θ

A: Given:

Q: Find the area of the region that's inside the curve r=cos2(Θ) and outsid the curve r=1+sin(Θ)

A:

Q: Find a parametrization of the tangent line at the point indicated. r(t) =〈cos 2t,sin 3t〉, t = π/4

A: Given :  r(t) =〈cos 2t,sin 3t〉, t = π/4

Q: Find the area of the region that lies inside the curve r = 2+ cos 20, but outside the curve r = 2+…

A:

Q: Consider a new curve Č parametrized by r(t) = (cos t esint, sin t- cos t), 0 <t <I but with F still…

A:

Q: Use Green's Theorem to evaluate | F. dř, where F = (Va + 4y, 2x + 9) C consists of the arc of the…

A:

Q: b) Use the polar coordinate to find the integral S+y) dxdy

A: See the attachment

Q: Use the arc-length formula of the parametric equation and evaluate the arc-length of the curve while…

A:

Q: Find the area of the region enclosed by the inner loop of the curve. r = 6 + 12 sin(0)

A:

Q: Parametrize the following curve: y = tan−1(x2 + 1)

A:

Q: Sketch the motion of a particle with position as: x = 5 sint y = ²/-nstsn - St≤n as tvaries in the…

A: We need to plot the motion of the particle, whose position is defined as: x=5sint, y=t2 in the…

Q: Find the points on the cardioid r = 4(1 – sin0) at which there is a horizontal tangent line, a…

A: According to the given information, it is required to determine the horizontal tangent line,…

Q: find the mside the r= 2a cos curve of region area the outside the r=Q arcle .

A: From given,we have to find the area of the region inside r=2a cos(theta) and outside r=a

Q: Calculate the length of the curve r=a*sin(^3)(x/3) for (x(1)=0, x(2)=3pi)

A:

Q: r=l+ cos 0 r= cos 6

A: We will answer the first question as we don't answer multiple question at a time. Please resubmit…

Q: Evaluate (2х — у) dx + (х + Зу) dy. C: arc on y = x72 from (0, 0) to (4, 32) 512/7

A:

Q: Evaluate |(2y+cos x)dx + (5x+ sin y)dy along the positively oriented curve C. C is the boundary of…

A: We have to evaluate the integral ∫2y+cosxdx+5x+sinydy along the positively oriented curve C. Where C…

Q: Calculate the integral ∫C(x2+y2)zds, where the curve C is parameterized by r(t)=(sin3t,cos3t,4t),…

A:

Q: - Find the aera under the curve y = cosx Form x = 0 to x = -fx sec² (ax² )dx a#0

A:

Q: Find the aera under the curve y = cosx fx sec²(ax² )dx a #0 Form x = 0 to x = 7/

A:

Q: Find the length of the curve. r(t) = cos(3t) i + sin(3t)j + 3 In(cos(t)) k, 0 <t< n/4 %3D

A: Find the length of the curve:…

Q: Sketch the regions enclosed by the given curves y-4 cos(7x), y- 4 sin(14x), x -D, x-/14 0.05 0.10…

A: The solution of above question is written below.

Q: Find the length of the curve. r(t) = cos(5t) i+ sin(5t)j + 5ln(cos(t)) k, 0<t< n/4

A: r(t)=cos(5t)i+sin(5t)j+5ln(cos(t))kWhere, 0≤t≤π/4

Q: Find the derivative 4cos4t sin4t O2cot4t O Other: -1/2 cot4t of the parametrically defined curve (t)…

A:

Q: 2. Let y be the curve in R3 given by t (t, 2 cos t, 2 sin t) for 0 <t < 47. Compute ds

A:

Q: Sketch the cardioid r = 3 cos 0 and find the coordinates of the points on the cardioid where the…

A: Given polar equation is r=3cosθ

Q: Use Green's Theorem to evaluate / F · dř, where F = (Va + 6y, 3x + y9) C consists of the arc of the…

A:

Q: Find the area enclosed by one loop of the curve. (Show all work separately and submit on HuskyCT…

A:

Q: Find where) i ) et u*rany tany = 1 , U= xInx (use chatn reule ) ii) coscxy) - * + e+y) = 2 yz

A:

Q: Consider the given curve: R(f) = (2 cos f, 12f +3,-2 sin f) Reparametrize the curve using arclength…

A:

Q: 3 dz where C, is the top half of circle with radius (b) Compute the upper bound of 2,

A:

Q: Q1. Find the length of the of the curve y = In(cos x) from x = 0 to x = . %3D

A: Explanation of the solution is given below...

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.