Find the area enclosed by the given ellipse. x=a cos t, y = b sin t, 0sts 2 The area is. (Type an expression using a and b as the variables. Type an exact answer, using t as needed.)

Q: find the length of the indicated portion of thecurve.r(t) = (et cos t)i + (et sin t)j + etk, -ln 4…

A: Given, r(t)=etcosti+etsintj+etk length L=∫-ln40r'(t)dt            .......(1) now derivate given…

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A: we have to find the area.

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Q: • Graph the cardioid r a(1 + cose), a <0? • Graph the cardioid r = a(1+ sin6), a < 0? Graph the…

A: Graph are given below:

Q: The area of the region inside r = 6 cos 20 the rose and outside the circle = 3/2

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Q: The common area between the cardioid r = 1+ cose and the circle r = 3cose is: Select one: (1+ cose)?…

A: For cardioid  θ=0,   r=1+1=2 θ=π2,    r=1+0=1

Q: Done Find the area between a large loop and the enclosed small loop of the curve r = 4 + 8 cos(30).…

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Q: Use the arc length formula 2 dx 2 L = dy dt dt dt to find the arc length of the curve. x = cos 12t,…

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Q: x² : 4ay from x 0 to x = 2a

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Q: O Graph and find the area inside the ellipse given by x = 4 cos t, y = 2 sin t, for 0<t< 27.

A: Please refer the attached image for complete Solution.

Q: Find the arc length of the following line. y = 2x+ 3; [0,3] Which of the following is a simplified…

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Q: 8. Find the area of the surface of revolution r = 2 cos 0 revolved about the π polar axis 0 < 0 <

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Q: Use integration and trigonometric substitution to find the area enclosed by the ellipse: x² y? = 1.…

A: From the given ellipse: x24+y216=1 So, x24+y216=1x-0222+y-0242=1center:(h,k)=(0,0)Major-axix &amp;…

Q: If the area of APQR is A, give the expressions that complete the equation for the measure of ZR. R…

A: We will use formula for area of triangle.

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A: Given, R=12 ∮∂Rxdy-ydx From the given figure on ∂R we have, rt=acosti^+bsintj^ that is on ∂R,…

Q: Find the area inside the lemniscate 2 = 6 sin(20) and outside the circle r= v3 A) B) %3! 3/3–T+6 3/3…

A: we find the area inside the leminscate  r2 = 6sin (2θ)and outside the circle r = v3

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Q: Which of the following is an arc length parametrization of a circleof radius 4 centered at the…

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Q: c) Find the curve length of the lemniscate of the area Inside the lemniscate r² = 6 cos 20 and…

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Q: Use integration and trigonometric substitution to find the y? = 1. area enclosed by the ellipse: 36…

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Q: Show that the surface area obtained when the arc of the parabola y? = 16az from I = 0 to r = h is…

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Q: Draw the curve r2 = 2a? $20, a > 0 and calculate the area enclosed by this curve COS

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Q: Use the formula area(R) = } for T dy – y dæ to find the area of the sector R of the ellipse that is…

A: Consider the provided question, We need to find the area of the ellipse that is swept out by the…

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Q: Find the area of the region enclosed by one loop of the polar curve r=4 cos(30). (See diagram 1…

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Q: 2) Use polar coordinates to evaluate ff, sin OdA with R being the region in the first quadrant…

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Q: For this problem, consider the polar curve r= 2 + sin(20), 0 s0ST/2. %3D (a) Find the area enclosed…

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Q: Q4 :- Find the area inside one leaf of the curve r=cos 20.

A: As per our guidelines we are allowed to solve one question at a time. Kindly repost the rest…

Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. = Vx, 1sys 5

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Q: Use a familiar formula from geometry to find the length of the curve described and then confirm…

A: Recall:  L=∫abr(θ)2+r'(θ)2dθ We have, r=7sinθ+2cosθ, a=0, b=π

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Q: axis from t = 1 to t = 4. Find its Find the area enclosed by the following parametric curves and the…

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Q: The parametric equations x = 4 - 5 sin 3t and y = 3 + 5 cos 3t for  0 ≤ t ≤ π/2  represent a curve…

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Q: Find the area inside the larger loop and outside the smaller loop of the limicon ? = 1 + 2 cos ?.

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Q: Use the arc length formula 2 dy dt dx L = dt + dt to find the arc length of the curve. x = cos 61, y…

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Q: Consider the ellipse + = 1. n/2 Show that the circumference of the ellipse is given by C 2 V4 cos? t…

A: According to our company's guidelines I can only answer first three subparts of the question since…