Evaluate the triple integral. 8z dv, where E is bounded by the cylinder y2 + z2 = 9 and the planes x = 0, y = 3x, and z = 0 in the first octant

Q: Evaluate the iterated integral. 4 1 v1-z seº dx dz dy 0 0 0

A: given  :

Q: Evaluate the double integral | x(1+y²)-1/2 dA; R is the region in the first R quadrant enclosed…

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Q: Evaluate the integral, where E is enclosed by the paraboloid z = 9 + x² + y?, the cylinder x2 + y2 =…

A: In cylindrical coordinates:-x=r cos θy=r sin θ z=z Also, x2 +y2 =r2  And, ∫∫∫f(x, y, z)…

Q: The value of the triple integral 2x² dV E where E is the region inside both x² + y? + z2 : z = -V3x2…

A: Here we will use cylindrical co ordinate to find triple integral  in cylindrical co ordinate  x = r…

Q: Evaluate the double integral Is = ĮS (2² – 2 =º) dxdy 2 z3 S where S is the region in the 4th…

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Q: Evaluate the double integral Is- (2 - 2 2) dxdy where S is the region in the 4th quadrant (y <0, z2…

A: Given the double integral and equation of curve I=∬Sx2−2x3dxdy And y−3x,y=−2x2

Q: Evaluate the following integral: b.) !!!! xyz dv if S is the region bounded by the cylinders ² + y²…

A: According tot the given conditions the limi values of x,y and z are0≤x≤50≤y≤25-x20≤z≤25-x2Hence…

Q: The improper integral A e B 0 C D) 1 + ∞ [** 0 e-x dx is

A: The given improper integral is: I=∫0+∞e-xdx

Q: Q.3 Find the double integral for L. x² dydx, where R between y = 1/x , y = x and x = 2 SR

A: From the given region, y varies from y = x  to y = 1/x and x varies from x = 1 to x = 2. The…

Q: a) Evaluate the given integral In y TT In z dz dx dy 1 1 1

A: Finding the given integral

Q: sketch the region of integration, and write an equivalent double integral with the order of…

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Q: Evaluate the triple integral. y dV, where E = {(x, y, z) | 0 < x< 8,0 s y s x, x – yszsx + y}

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Q: area ZA (xy) dx dy y/3 10.

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Q: I.Evaluate the ff. iterated integrals. • rel /2 ptan y sec y 1. x'cos' ydxdy

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Q: Evaluate the iterated integral below. π/4 1 Só S"!+S": 0 0 y cos (x) dy dx

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Q: Evaluate the integral (x + z) dS where S is the part of the cylinder y + z2 = 4 with x E [0, 9].

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Q: Let D be the shaded region below. What is the minimum number of iterated integrals that we need for…

A: Minimum no. Of iterated integrals are 2.  (Last option)

Q: Evaluate the integral. integral y e 2y dy

A: Evaluate ∫ye2ydy

Q: Evaluate the double integral. y dA, D = {(x, y) | 0 s x s 2, 0 sys Vx} x2 + 1

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Q: 2. Evaluate the following iterated integrals. (») L rey dy dx In(a² + y? + 1) dx dy (b) 4- y

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Q: s) Evaluate the triple integral, 1– y – 2) dV where E is the region given by E = {0SES y, 0<y< 4,…

A: Solution

Q: evaluate the triple integral given by fff (x + 2y)dV, where E is bounded by the cylinder y = x² and…

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Q: 14 Find the integrals using integration by parts. xp_ († +x)xf • - dx c. fr'e"de e flnx'de d. f (in…

A: Solution: The objective is to find the value of the given integral

Q: Evaluate the following integrals. 1 (a) dz dy dx. e (b) TI Vx2 + y2 dV, where E is the solid in R3…

A: we have to find the integrals 1) ∫01∫01∫y1e-z2dzdydx 2) ∫∫∫Ex2+y2dV,where E is solid bounded…

Q: Evaluate the double integral I3 = S (21 – 4 2*) dxdy S where S is the region in the 4th quadrant (y…

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Q: 1 Draw the region over which we are integrating, change the order of integration (that is, write…

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Q: 5. Evaluate the iterated integrals. a. b. [²³² (x+y)dx dy S S S xyz dx dy dz

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Q: Q.3 Find the double integral for L. x? dydx, where R between y = 1/x ,y= x and x = 2

A: From the given problem:   I=∫∫Rx2dydx   And curves are: y=1x; y=x and x=2   So the bounded region is…

Q: 3 The integral ³³ g(x, y) dxdy is equivalent 3 to ₁ ³x g(x, y) dydx

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Q: 1. Evaluate the integrals and sketch the region of integration. 1) º, S(+y +1)dædy 2) So , 1 sin…

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Q: ∙1 Ꮭ ᏝᎽ 1-x-y z dz dy dx

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Q: Evaluate the iterated integral below. π/4 1 S. S'y co Só 0 0 y cos (x) dy dx

A: Solution…

Q: Evaluate the double integral x° dA, where D = {(x,y) : 1 < x < e, 0 < y < In x}.

A: Evaluate the double integral as follows.

Q: 3. Show that, in the region D: 1< x<e, 0<y<In(x), the following double integral 3e4 + 1 x3 dA 16

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Q: 2 ytz dy dz Evaluate the double integral : 0.

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Q: (0,2) y =v4-x A (4,0) Which of the following double integrals has bounds that represents the region…

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Q: Evaluate the iterated integral. 1 2r y 8ry: dz dy dx

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Q: 4. Compute cach of the following iterated integrals by reversing the order of integration. sin (r)…

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Q: 5/ change the cartesian integral in an equvalant polor integral then evalute 2x-x² the polor…

A: Given integral ∫12∫02x-x21x2+y22dydx. The objective is to evaluate the integral. First we change x…

Q: Evaluate the iterated integral. 18 5 (x + y²) dx dy

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Q: Q.3 Find the double integral for SI, x? dydx, where R between y = 1/x,y x and x = 2

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Q: Evaluate the double integral for R: 0<y<1,0<x<y² . Sly e*dxdy .

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Q: 1. Use Numerical methods to approximate the following integrals (a) (x +y)dxdy , n = m = 3

A: Trapezoidal rule: ∫cd∫abf(x, y)dxdy=h2fa, y+2fa+h, y+fa+2h, y+⋯+fa+n-1h, y+fb, ydy, where h=b-an.…

Q: Evaluate the double integral x* dA, where D = {(x, y) : 1 < x < e,0< y< In x}. %3D

A: The solution is given as

Q: Approximate the integral fe* cos xdx using the composite Trapezoidal rule with M=5 subintervals. M-1…

A: The given integral is ∫01excos xdx. Approximate the integral ∫01excos xdx using the composite…

Q: Evaluate the iterated integral below. π 1 4 S*S'y cos (x) dy dx Só 0

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Q: Evaluate the iterated integral. Triple Integral: (Outside to inside) Integral from 1 to 7, Integral…

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Q: Evaluate the iterates integrals 2) r*dA D = {(x, y) : 1 < a <e, 0< y S In(x)}

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Q: Evaluate the following integral: a.) SIS z ln y tan z dV if S = {(x, y, z) = R³ : − 1 ≤ x ≤ 0, e ≤ y…

A: S is a rectangular cuboid, hence limit of each individual are independent so the integral are…