( b). Je2cos (πx) dx .

Q: Y – 5x |dA 100 cos x + y

A: We have to evaluate the double integral ∬100cosy-5xx+ydxdy over the region D where the region D is a…

Q: Evaluate the iterated ntegral by Lonverting to polor coordinates. 2. zy dx dy 34

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Q: Given the double intergral 3 S.³ To √²+y² Evaluate the above dy dx intergral using cartesian…

A: some of the formula of integration . ∫1x2+a2dx=ln|x+x2+a2|+C∫xndx=xn+1n+1+C

Q: Use spherical coordinates to evaluate the triple integral /|| 2² + y² + 2² dV, where E is the ball:…

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Q: Find the total arc length of the cardioid r=1+cos6O

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Q: Find the area enclosed by the ellipse x = a cos t, y = b sin t, 0 ≤ t ≤ 2π.

A: Given Data The first equation of ellipse is x=a cos t. The second equation of ellipse is y=b sin t.…

Q: Evaluate the integral x² dx + y? dy where C consists of the arc of the circle x2 + y² = 4 from (2,0)…

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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 work done W,to stretch a spring from its natural length to an extension of 6 meters Is given 6.…

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Q: The folium of Descartes is defined impliciHy as given nee here a) determine dy dx

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Q: Q sketch the region of in tegration and evaluate the a) 3 yxy e'dxdy

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Q: Find the surface area of the figure generated by revolving x = 6 cos(t), y = 6 sin(t) where 0 <ts…

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Q: If the area enclosed by the curve x = 4 cos³ t and y = 4 sin t (wheret e R) is A then what is A?

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Q: Find all finchons Man sanisty he Mowing inihal problim dy %3D dy dx =4 ex ーメ how mam solwhin does t…

A: Given,           dydx=y2e-x    and y(0) = 12

Q: 1 Evaluate dV, where E lies between the spheres a? + y? + z? 25 and + y² + z? x² + y? + z? = 36 in…

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Q: Use SphericalL coerdinates to evaluate the +र |राज्ट | . triple integral SSS x°*y@;=? d V, Where E…

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Q: If the joint pdf of X and Y is 1 fx.y(x, y) 2no? find the mass in the circle, x² + y? <a?.

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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: Use cylindrical coordinates. Evaluate |/| 6(x3 + xy²) dv, where E is the solid in the first octant…

A: We have to evaluate the integral ∬∫E6x3+xy2dV, where E:z=4-x2-y2 in the first octant.

Q: The integral /4x? + 4y? + 42² dV тп, R where R is the solid hemisphere with x? + y? + z² 0 Find the…

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Q: 5. Use spherical coordinates to evaluate the triple integral ///+y²+²dV, where E is the ball: x? +y?…

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Q: Find the arc length of the cardioid r = 2 – 2sin©.

A: Given that: r=2-2sinθ Differentiating with respect to theta,…

Q: the EXACT Salutian to the equation belaw/de not decimal apprakimatea) give %3D

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Q: 3) Evalnete the itevated integral by Converting the to polar corrdinate, a) dy dx

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Q: Find the area of the region enclosed by the curve r = 2+ cos (20). (1.) (3,( Bu Die Aya Yard 97…

A: To find the area of the region enclosed by the curve r=2+cos2θ

Q: Use polar coordinates to evaluate the double integral 2 1 – a²- dy dx. (1+æ? + y²)²

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Q: Show that the area of the surface of the solid generated by revolving the cardie r = a(1- cos 0)…

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Q: How exactly do I work out/set up this problem to get my answers?

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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: Evaluate tot? xe*< + y2 + 22 dv, where E is the portion of the unit ball x2 + y² + z2 s 1 that lies…

A: Triple integral

Q: Solid Con Sist of ight hi aud a cylinder of hrinlt ha the dim ensieua

A: In this question, the concept of the derivative is applied. Derivative A derivative can be used to…

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

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Q: Is it true that Arg(z) = arctan for x + 0, where x = Re(z) and y = Im (z) ?

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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: Date: ) By the changing the Following double integrals ot to Polar coordinate, evaluate र' ²+y2 dy…

A: Given

Q: (a) y = arctan (b) y = v1-x' arsin(x)

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Q: Find the basocble for y (x) = x Values of Pasometer d ahich, slation of DEs dy is %3D

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Q: l, arctan( y/x) dA, where R = {(x, y) |1<x° + y° < 4, 0 < y< x} %3D

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Q: Compute the double integral // Vx² + y² dA where D is the part of the first quadrant lying between…

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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: Change the integral from rectangular to polar. Then evaluate. 1 dy dx 36-x² 1 + Vx2 +y?

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Q: Evaluate the integral S 4-y2 dx dy using polar coordinate

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Q: Use geometry or symmetry, or both, to evaluate the double integral. (8x + 2)dA, D = {(x, y) | 0 sys…

A: Given Data The double integral is ꭍꭍD (8x+2)dA The interval is 0≤y≤√36-x².   Let, The interval of…

Q: \ Compute dx using the (a) Trapezoidal rule

A: 6.(a)  Given function is ∫-11e-x2dx Trapezoidal rule ∫abfxdx≈∆x2fx0+2fx1+2fx2+2fx3+........+fxn…

Q: Find dyldy and xz4 Sint, y² Scost, OCtca24 For which vakes Of t is Hhe cure concave puars? anguer n…

A: x=4sint  , y=5cost

Q: The area of the region enclosed byy = 8+|cos , y = 8, z = 27 and z = 117 is

A:

Q: Given fS (x,y)dA = [ S. 5xy dydx. (i) Sketch and shade the region R,

A: see below the answer and figure

Q: Convert to cylindrical coordinates and evaluate the integral 5 /25–x² 6 !!! dzdydx x² + y- 0 0 0

A: Conversion of cartesian co-ordinates into cylindrical co-ordinates. φ is angle made by vector with…