3-y Consider S°"(3x² + 2y)dxdy A) Sketch the region R B) interchange the order of integration C) Evaluate

Q: (c) Write the integral 3 2 + hpæpzp z + „h in spherical coordinates. Do not evaluate the integral.

A: We will find out the required solution.

Q: Using polar coordinates, evaluate the integral /| sin(x? + y²)dA where R is the region 4 < x? + y? <…

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Q: Use cylindrical coordinates. Evaluate II Vx2 + y? dv, where E is the region that lies inside the…

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Q: Find using spherical coordinates integration zVz? + x² + y²dzdydx VA-x² Jo

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Q: V4-r2 Convert the integral (S" S S" rdzrdrde) to rectangular coordinates and spherical coordinates.

A: A coordinate system is a convention that is used to represent a point uniquely using a set of…

Q: Sketch the region R in the first quadrant between the circles (x – })° + y² = } and (r -)? + y? = .…

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Q: sin y dV, where E lies below the plane z = x and above the triangular region with vertices (0, 0,…

A: Given, the region E lies below the plane z = x and above the triangular region with vertices 0,0,0,…

Q: Use cylindrical coordinates. Evaluate II Vx2 + y2 dv, where E is the region that lies inside the…

A: Volume using triple integral

Q: Find the v o l um e generated by rotating the region bounded by the curves y = ex, x = 0, y = pi abo…

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Q: Find the moments of inertia of the region given in the figure about the x and y axes. Ix=? Iy=?…

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Q: Use cylindrical coordinates. Evaluate III Vx2 + v² dV, where E is the region that lies inside the…

A: We have to evaluate ∭Ex2+y2dV, where E is the region that lies inside the cylinder x2+y2=9 and…

Q: Using polar coordinates to evaluate (3x + 4y) dA, where R is the region in the upper half of the…

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Q: Evaluate the line integral g. xy? dx + 2x²y dy, where C is the triangle with vertices (0,0), (2, 2),…

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Q: Sketch the region of integration and evaluate by changing to polar coordinates: 6 • f(æ) 1 dy dæ /x²…

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Q: a) Use polar coordinate to calculate dA, R V3r where Ris the region bounded by y = V1- x, y = -x and…

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Q: Using polar coordinates, evaluate the integral sin(x? + y?)dA where R is the region 16 < x2 + y² <…

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Q: Use cylindrical coordinates. Evaluate II V² + y2 dV, where E is the region that lies inside the…

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Q: OUTM a) Use polar coordinate to calculate dA, V3r where Ris the region bounded by y = I-7y = -r and…

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

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: Using polar coordinates, evaluate the integral sin(x? + y)dA where R is the region 9 < x² + y? < 25.

A: Answer and explanation is given below...

Q: Use cylindrical coordinates. Evaluate x2 + y2 dV, where E is the region that lies inside the…

A: The integral given is ∫∫∫E x2+y2 dV For the cylindrical coordinates x=r cos(θ)y=r sin(θ)z=zdV=r dz…

Q: 338. [T] Use a CAS and Stokes' theorem to approximate line integral /[(1 + ykdx + (1+ z)xdy + (1 +…

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Q: Find the areas of the shaded regions in Exercises 61–64. 61. y = 2 y = 1 + cos x п 62. y = sin x х…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Use cylindrical coordinates. Evaluate 2x(x2 + y2) dV, where E is the solid in the first octant that…

A: To convert from rectangular coordinate system to cylindrical coordinates system, use the conversion…

Q: Use cylindrical coordinates. Evaluate Vx2 + y2 dv, where E is the region that lies inside 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: Use spherical coordinates to evaluate the triple integral e-(+y?+2?) dV, 2+ + 22 where E is the…

A: Using spherical coordinates to find the triple integral.

Q: 2yx dA ; R={(x,y):0sxs1,-1<ys2} y+3

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Q: Use cylindrical coordinates. JSS x² + y2 dv, where E is the region that lies inside the cylinder x²…

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Q: x dA; R is the region enclosed by y = sin-' x, %3D x = 1//2, and y = 0.

A: Let I=∬RxdA  We need to evaluate I=∬RxdA over region R enclosed by y=sin-1x, x=12  and y=0

Q: b) Evaluate the contour integral i ΙΣ where C {z : |z - i| = 3} and oriented counter clock-wise.

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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: 5. Use spherical coordinates to evaluate the integral , z dV where E is the region between the…

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Q: UTM a) Use polar coordinate to calculate dA, R V3r where Ris the region bounded by y = v1-r,y=-r and…

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Q: Find the area of the plane z = 4x+y for all (x,y) ∈ R where R is the region in the first quadrant…

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Q: Use cylindrical coordinates. Evaluate 3(x3 + xy2) dV, where E is the solid in the first octant that…

A: Given: The solid E is in first octant that lies beneath the paraboloid z=1-x2-y2.

Q: Evaluate the integral 1 V1-y² V2-x²– y² (x² + y? + 2?) dzdxdy 2+y² by changing it to spherical…

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Q: 5) 2z dV, E is the solid enclosed by the cone % = Vr2 + y? and the E plane z 5

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Q: Use cylindrical coordinates. Evaluate II| Vx² + y2 dv, where E is the region that lies inside the…

A: We have to evaluate  ∭Ex2+y2dV, where E is the region that lies inside the cylinder x2+y2=1 and…

Q: Find the area of the plane z = 4x + y for all (x, y) = R where Ris the region in the first quadrant…

A: Consider the equation of the plane, z=4x+y for all x,y∈R,where R is the region in first quadrant…

Q: xy dA RVX² + y² a.) from Cartesian coordinates to polar coor- dinates where the region R is given on…

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Q: Evaluate Triple Integral H (6 − x2 − y2) dV,  where H is the solid hemisphere  x2 + y2 + z2 ≤ 16,…

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Q: Evaluate the double integral f(r, 0) dA. * Tt/2 (7 cos(0) r dr de -T/2 Jo Sketch the region R.

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Q: UTM Use polar coordinate to calculate dA, V3r where Ris the region bounded by y = V1 –7,y = -r and y…

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: Use cylindrical coordinates. Evaluate II 5(x3 + xy2) dv, where E is the solid in the first octant…

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Q: UJ OUtall a COIIIIUCICE Imerval Ior po. Show that Oi – y) = , ới – y)? +E, Vi – ŷ;)² %3D |- %3D1…

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Q: Use cylindrical coordinates. Evaluate || Vx²+ y? dv, where E is the region that lies inside the…

A: The given integral is: I=∫∫∫E x2+y2 dVwhere E is the region bounded by: x2+y2=4 and between planes…

Q: Use polar coordinates to evaluate S (5x-y) dA gion in the fourth quadrant bounded by the circles nd…

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Q: 2. Use polar coordinates to evaluate If y² dA, R where R is the region bounded by the line y = x,…

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Logic and Proofs

Discrete mathematics deals with the separated values of data such as integers. It is widely used in the practical field of computer science and mathematics. By knowing discrete mathematics one can improve their reasoning and problem-solving capabilities. Discrete mathematics became popular after the boom of computers which operate in discrete steps and store data in discrete bits. It also useful in studying computer programming, algorithms, and cryptography.