ind the surface area of the sphere given by x = a sin 0 cos o, y= a sin e sin qP, z=a cos 0, 0s0sn,0sos 2n.

Q: Determine the area enclosed by the following curves r = 2 + cos 0 97/2 r = 4 + 3 sin 0 7/12 + v3/16

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Q: (4) Find the surface area of the cone S a) b) c) d) 7-√√2 5-√3 p(r, 0)=(r cos 0,r sin 0,r) for 0≤0…

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Q: Find the area bounded by the trigonometric curves Ⓒ 3.450 square units O 2.828 square units O 1.414…

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Q: Let P(cos t, sin t) be a point on the unit circle x2 + y2 = 1 in the first quadrant. Show that t is…

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Q: Find the area inside the oval limaçon r=7+3 sin 0. The area inside the oval limaçon is (Tuno uor…

A: we have to find the area.

Q: 2 | – j|² dz Z + 1 C

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Q: find the area of the surface S: x² + y² + 2² = 4 -A <tan -^ (*) FO 6 < COS Cos FJ VI (2) 4 DEX TI 3…

A: The given Surface is                    x2+y2+z2=4 ........1where π6≤tan-1yx≤π3 and π4≤cos-1z2≤3π4…

Q: Find the area in the first quadrant inside the curve r = 4 + cos 2θ but outside the curve r = 3 cos…

A: Given  The outside the curve r = 4 + cos 2θ but inside the curve r = 3 cos 2θ . Formula for area…

Q: Find the area outside "r^2=9cos(2theta)" and inside "r=2-cos(theta)"

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Q: Find the area enclosed by the given parametric curve and the y-axis. sin²(t), y = 8 cos(t) X = y 0.2…

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Q: Calculate the value of x in the figure: AB = BC = DA and BD = DC (Not drawn to scale). %3D %3D 21 2x…

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Q: Find the area Inside the cardioid r=2 cos (6/3) and outside the circle of radius r = vZ centered at…

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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: O show mat me Nomal point @ X= a( Coro +o Smo) y= a(8in0-o Cor0) dy Sine %3D ep" of Normal S-ゴ」=…

A: the parametric function is x=a(cosθ+θsinθ) y=asinθ-θcosθ Differentiate each with respect to theta…

Q: Find the area of surface revolution, when x=1+cosθ. , y=sinθ Where 0≤θ≤2π

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Q: Find the areas of the regions . 1. Inside the oval limaçon r = 4 + 2 cos u 2. Inside the cardioid r…

A: Replace the variable u with θ The area inside the oval limaçon is given as, Where, a=0 and b=2π…

Q: Find the area of the region that lies inside both curves. r = 5 + 3 sin(?),    r = 5 + 3 cos(?)

A: The area between two polar curves, say r=f(θ)  and  r=g(θ), within the limits θ=α  to  θ=β is given…

Q: If the area enclosed by the curve a = 7 cos t and y = 7 sin t (where t e R) is A, then what is A?…

A: If the area enclosed by the curve x=7cos^3t and y=7sin^3t (where t∈R) is Aπ8, then what is A?

Q: sin(z) Evaluate the integral Tz+1)(2² + 2) dz where C is the circle |z – 2i| = 1.

A: We have to evaluate the integral ∫Csinzz+1z2+2dz where C is the circle z-2i=1

Q: Find the area enclosed by the curve r V6(1 – sin®). %3D

A: First we will plot the curve and and using Double integration we will find area bounded

Q: Find the length of one arch of the cycloid 2(t – sin(t)), y = 2(1 – cos(t). х

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Q: Find the area of the surface formed by revolving the circle r = f (0) cos 0 about the line θ = π/2.…

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Q: V-cot? u +4cot u –1 du = ? integralini hesaplayınız. sin?

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Q: Find the area of the surface over the given region. The sphere, (u, v) = 10 sinu cos vi+10 sinu sin…

A: Introduction: When the surface is provided is parametric form, the surface area is determined…

Q: Find the length of one arch of the cycloid 8(t – sin(t)), y = 8(1 – cos(t)). %3D

A: Given: x = 8(t -sint(t)) y = 8 (1-cos(t)) To find the length of arc.

Q: ind the arclength of the curve over the given interval. (a) r = 1 + sin θ, 0 ≤ θ ≤ 2π (b) r = 4 sin…

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Q: 29. Area = %3D EF, FH, and HI are tangents. EI is a diameter. E 2ft.F J 8ft. H

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Q: If the area enclosed by the curve z = 5 cos t and y = 5 sin' t (where te R) is A- then what is A?…

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Q: If the area inside both the cardioid r 6 + 6 sin 0 and the circle r = 6 is A + B-, then what is %3D…

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Q: Find the area of the shaded region. r = sin(20) r = 4+3 cos (8)

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Q: Find the area inside the oval limaçon r = 6 + sin 0.

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Q: Use Green's Theorem to evaluate the integral Sc(5 sin y – 3y, 2 + 5x cos y) · dĩ (6) where C is the…

A: (6) Use Green's Theorem to evaluate the integral ∫C5sin(y)-3y,2+5xcos(y)·dr→, where C is the line…

Q: Find the areas of the regions Inside the cardioid r = a(1 + cos θ), a &gt; 0

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Q: The area of the region inside the circle r = 6 cos e and outside the cardioid r = 2(1+ cos 0), a > 0…

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Q: 1. Draw the curve r² = 2a? cos 20, a > 0 and calculate the area enclosed by this curv

A: This question is about application of integration in polar coordinates

Q: Find the area which is outside the curve r 4 cos 20 but inside the curve %3D r = 2.(

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Q: Use Green's theorem to evaluate $y – sinx)dx + cosx dy Where c the triangle of the adjoining figure…

A: Green`s Theorem:-  Green`s Theorem states that the line integral is equal to the double integral of…

Q: Find the diih of y integral tanar 230 e dn dy a) | shso b) c) O sysl-z 1-2 d) Nove of theoe

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Q: Find the area under the curve for the parametric function defined by the equations x(t) = -2 cos t,…

A: Given: xt=-2cost  , yt=3sint , 0≤t≤π2 Formula used: The area under a parametric curve: A=∫abytx'tdt

Q: JT 9 cos' t and y 9 sin't (where t E R) is A- then what is 8. If the area enclosed by the curve x =…

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Q: the wire that lies along the curve Di + (7 sin t)j. 0sts5 Osts1; 8= 5? its

A: We have to find the mass of wire according to the given information

Q: If zy + sin y + arctan(z) = then what is the value of at (1,0)? a)-1 b) 1 C) 0 d) -2 e) 2

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Q: 36. x = sin t, y= sin t cos t, 0<t<T/2

A: Here x=sint and y=sintcost where 0≤t≤π2we have to find the area enclosed by parametric…

Q: sin z 0 dz, where C is the positively oriented circle of radius 1, |z| = 1. %3D

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Q: The region enclosed by the curve r= 4 cos e

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Q: Use Green’s Theorem to evaluate ∮C squre toot of (1 + x^2)dx + 14x dy, where C is the triangle from…

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Q: The area of the region inside the circle r = 6 cos 0 and outside the cardioid r = 2(1 + cos), a > 0…

A: Given: the circle r =6 cos θ and the cardioid r=2(1+cosθ )

Q: Find the area under the parametric curve x= 2(t + cos t), y=2(1 - sin t) from t=0 to t= pi.

A: We have to find the area under the parametric curves whose equations are : x=2t+cos ty=21-sin t…

Q: By revolving the semicircle x = r cos t, y = r sin t. (0 ≤ t ≤ π) about the x-axis, show that the…

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Q: Find the length of the entire perimeter of the region inside r = 6 sin 0 but outside r = 1.

A: Given that  r=6sintheta and r=1 To find the length of the entire perimeter of the region