Evample: y-xy, Yu)=1 and h:o.l a pproximale Y(1 3) using improved Euler Muthocd.

Q: Verify Green's Theorem by evaluating both integrals Lv² dx + x² dy dA ax ay for the given path. C:…

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Q: Evaluate the triple integral. 3xy dV, where E is bounded by the parabolic cylinders y = x² and x =…

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Q: w= Pcxiy,Z) = In (x+y+2) ,x= cost, and z = 4VE %3D 2X = y= Sint >use ch ain rule to Rind du in terms…

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Q: The differ en tial equation yʻz + 2y'e* = 0 is (a) linear (b) separable (c) homogeneous (d) exact

A: The given differential equation is: y4x+2y'ex=0

Q: Use Simpson's Rule and all the data in the following table to estimate the value of the 28 integral…

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Q: Evaluate the improper iterated integral. x2 dy dx 1 + y?

A: The solution is given in the next step.

Q: Evaluate the triple integral. 2xy dV, where E is bounded by the parabolic cylinders y = x² and x =…

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Q: in integating the function fxcos(3r) de using integration by parts, what would you choose for your…

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Q: 5z dv, where E is bounded by the cylinder y2 + z2 = 9 and the planes x = 0, y = 3x, and z = 0 in the…

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Q: find the derivativa dy for the frurrtion y=x by using lagarithmic differatiation.

A: Given y=x5x Taking logarithmic both sides, lny=lnx5x implies lny=5xlnx

Q: 1. Under the paraboloid = 3z2 + y? and above the region bounded by y = x and r= y² – y

A: Find point of intersection of:  y=xx=y2-y y=y2-yy2-2y=0y=0,2

Q: b) Estimate the integral esindx using composite traperoidal rule with h= 0.25.

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Q: To evaluate the integral fx e²dx using integration by parts, the best choices for u and dv are: Oue,…

A: The objective of the question is choose the correct option for integration by parts.

Q: The integral. 1 dydx is VÆ V10 – y3

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Q: To integrate y3xdx we apply integration by parts and in the form u dv, u is set as:

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Q: Consider the triple integral I = S S“(y² – 6z)dydzdx. -

A: ∫02∫x21∫0xzy2-6zdydzdx=∫02∫x21z3x33-6z2xdzdx=∫02x31-x812-6x13-x63dx=31.88888…

Q: Evaluate the double integral. /| 6xy2 dA, D is enclosed by x = 0 and x = V4 – y-

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Q: Evaluate fz² In z dz using integration by parts 2 Onz-+ +c Oz-+ Onz-+c Oz² Inz - 2 + c

A: ∫z2lnzdz=∫(lnz)z2dz=(lnz)z33-∫1zz33dz+c=(lnz)z33-∫z23dz+c=(lnz)z33-13z33+c=(lnz)z33-z39+c=z33(lnz)-z…

Q: Compute the irertia móment by x ( Ix=Sy?JA) tor number off segment n=s hyte multple-trapezoidal…

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Q: use secant method to to goproximate the solut ion of accurate to within 10, assuming X. = 1.5 and X,…

A: Use the following formula, to find the approximate root of the equation fx=0 by the secant method.…

Q: 1 Evaluate dV, where E lies between the spheres x + y + z = 16 and + y? + z2 = 64 in the first…

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Q: Integrate fcx)9,2) =X+y -Z over thep Poth from OLo.0.0) to A (2,1,2) given by, ostsi (C) = r z i…

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Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=0,…

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Q: Evaluate the triple integral. 4x dV, where E is bounded by the paraboloid x = 5y2 + 5z2 and the…

A: We have a paraboloid, and each cross section is a circle, parallel to the plane x = 5. We use…

Q: se Usa Grean's Thaoram to ecaloate the boundary of the region (travarsad cantarclodase) acadrant…

A: Given data-                   ∫c( ex + y2)dx +( ey + x2)dy. Where, e = Boundary of the region. We…

Q: find the indicated extrema, assuming that x, y, and z ar = xyz z - 12 = 0

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Q: Evaluate the triple integral. 10x dV, where E is bounded by the paraboloid x = 5y? + 5z2 and the…

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Q: Find the Particuldr int egral Por the giren egh giren eqn dzy + 16y -4X + COS4X ニ

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Q: Evaluate the triple integral. 7x dV, where E is bounded by the paraboloid x = 5y2 + 5z2 and the…

A: Here, E is the surface boiunded by the  paraboloid x=5y2+5z2 and the plane x=5. Now, at x=5,…

Q: Evaluate the integral (12x + 15y)dx + (24x – y)dy along the paraboli arc y = x from (0,0) to (1,1).…

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Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=0,…

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Q: Change the order of integration and hence evaluate o Sa ²(xy)dydx.

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Q: Apply Green's Theorem to evaluate the integral (4y² dx + 4x² dy), where C is the triangle bounded by…

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Q: is the follecing dif Mantial opuatíon Jmeo on mot Y with x>1. ey-x

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Q: Solve the DE, dy =y²-a? E, = , using the homogeneous method. ry (a) Hint: Rewrite the RHS as 2 -…

A: dydx=y2-x2xy⇒dydx=y2xy-x2xy⇒dydx=yx-xy⇒dydx=yx-yx-1 Now put, y=vx⇒dydx=v+x·dvdx

Q: The integral JJI eV 4x2 + 4y² + 4z² dV = mt, where R is the solid hemisphere with x2 + y? + z² < 11…

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Q: The line integral x dy – y dx Jc x2 + y? is independent of path.

A: Given integral is ∫Cxdy-ydxx2+y2.

Q: Evaluate the iterated integral. rIn(x) xe-Y dy dx dz 4z 434 3

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Q: c) Evaluate Ssin 3.xcos 4x dx by using integration by part.

A: Here we have to find            ∫ sin 3x cos 4x dx Integration by parts formula is          ∫ uvdx =…

Q: With integration by parts, J udv · Judv = UV - O True O False

A: Solve the following problem

Q: Evaluate the triple integral. 8x dV, where E is bounded by the paraboloid x = 2y2 + 2z2 and the…

A: The objective is to evaluate the triple integral ∫∫∫E8xdV, where E is bounded by the paraboloid…

Q: The value of the double integral a x dn dy is 0,

A: To find ∫-aa∫0a2-x2x dx dy : ∫-aa∫0a2-x2x dx…

Q: 3, Let R be the of: y: sinx region endlosed bu the grophs n enclosed by and 1 x70 . Groph R and…

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Q: A sphere of radius 2 cm contains a volume charge density Pv given by py = 4 cos“0 [C/m³]. Find the…

A: Given: Radius of the sphere=3 cm Charge density, ρv=4 cos2θ C/m3

Q: Evaluate the triple integral. 10x dv, where E is bounded by the paraboloid x = 2y² + 2z2 and the…

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Q: 3xy dV, where E is bounded by the parabolic cylinders y = x² and x = y and the planes z = 0 and z =…

A: It is given that, y=x2 and x=y2 and the planes z=0 and z=7x+y. Define the region E as follows.…

Q: Evaluate the integral / (12x + 18y)dx + (12x – y)dy along the paraboli - arc y = x² from (0,0) to…

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Q: Find the exuct Sulutivn for y'=x+2Y

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Q: If we rotate the region under the curve y = 8 between x = 2 and x = 3 about the x-axis, what answer…

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