tind the value of the consrant (min) that makes the D-E j X dx -CyfmX) dy so (Homogeneous, exact, separable Qud Linear)

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

A:

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: wnich of the followi ng functrons is homogeneous? 5x - 12メy ty? Po.) sm xy Ci) eln xy 2

A: To find which of the following function is a homogeneous function. A)fx, y=5x3-12xy+y3B)fx,…

Q: et What is the integrable form of dx? e* - e -X A) du B) du (c) и?—1) 2 du D [(1-u?) du

A:

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

A:

Q: Consider the integral dx I = 3 x+2 The approximation of I using the two-point Gaussian quadrature…

A:

Q: check if it is homogeneous and to what degree (3x - cosy)dy t_x' dy =0

A: Find your answer below

Q: Evaluate the double integral. 4y dA, D = {(x, y) | 0 s x s 1, 0 sysx} 6x + 1

A:

Q: 2-x 2-x-y (d) 0 Jo dz dy dx

A:

Q: Q1. Evaluate the integral, xy dv ху dV E where, E lies between spheres x? + y? + z? = 1 and x? + y +…

A: According to question,Given E lies between spheres,x2 + y2 + z2 = 1,andx2 + y2 + z2 = 2,for z≤0,

Q: Evaluate the integral f. x'y°dy – x³y'dx, where C is the square determined by the lines x = 0, y =…

A: We have to evaluate the given integral.

Q: Evaluate the triple integral. y dV, where E = {(x, y, z) | 0 < x < 5, 0 < y s x, x – y < z s x + y}

A: To evaluate the given triple integral.

Q: Evaluate the triple integral ||//. z°e" dV where E is bounded by the parabolic cylinder z = 16 – y?…

A: The volume of a solid can be calculated using the triple integrals. The unit dV can be written as…

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

A:

Q: ム)Find the solution f zhe intiol Volue Poblem Siven below by using Lapiece Tronsform the method.…

A: We have to use Laplace transform Method and basic formulae in Laplace we get general solution.

Q: (c) Estimate the following double integral: (x + y + 10) dz dy, D where D = {(x, y) | a² +y? < 4}.

A:

Q: The double integral T f(x)g(y)dydx,where a,b.c, and d are constants, is equal to

A:

Q: Evaluate the triple integral x dV where E is the solid bounded by the paraboloid x = 9y² + 9z2 and x…

A: Given the region

Q: The integral f[lR V16x2 + 16y2+16z²dV = mT where Ris the solid hemisphere with x? +y? + z² < 25, and…

A: The given integral equation is: ∫∫∫R 16x2+16y2+16z2 dV=mπwhere R is the solid hemisphere with…

Q: İTESİ Evaluate the following integral UNIV sin(x – y) dA, cos(x + y) where R is the triangular…

A:

Q: The value of the integral oIm(iz)dz, where C:| z|= 2, counterclockwise, is

A:

Q: The value of the triple integral (x² + y )dV where E is the E portion of x + y + z? = 4 with 0 < y,…

A: Solution:-

Q: For what value. of4, the fundion Ux)= I+dx is. solution of %3D the integral equation x3= Ut dt

A: We have to first transform the x variable of u function to t.

Q: Evaluate the triple integral a dV where E is the solid bounded by the paraboloid a = 10y² + 102² and…

A:

Q: a dV E where E is bounded by the cylinder a? + y? = 9, 0 0.

A:

Q: Evaluate the triple integral. y dV, where E {(x, y, z) | 0 < x < 2, 0 < y < x, x – y < z < x + y}

A:

Q: Evaluate S Jf3zdV E where E is the solid enclosed by z=1 =D1 and z = x + y O 4T O 27 О Зт

A:

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: Set up but do not evaluate, an integral for the length of y = Vr +2,1<r<7 using, 2 dy dx (a) ds = 1+…

A:

Q: The solid S is obtained by rotating the region enclosed by y = f(x) 2 0, a = 5+ 5e6 1- e6 5+ 5e16 1-…

A: The given question is solved below.

Q: Use the indicated change of variables to evaluate the double integral. 56xy dA x = 1/2 (u + v) y =…

A:

Q: The linear DE.s is called homogeneous if * R(x) is equal zero True O False O

A:

Q: Evaluate the triple integral 2xe" sin z dV, where Q is the rectangle defined by Q = [(x, y, z)| 0…

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Q: Given S J. 2. dy dx Rev erve the or der and ev aluate . Show Of Integration the region.

A:

Q: Given the area bounded by the parabola x² – 4x + 12y- 20 = 0, the x- axis and the lines x = 1 and x…

A: Sol

Q: (a) ( Evaluate the triple integral SI: z dV, where E E={(x,y.z):0<x<2,0<y<2.0<zく3).

A: Given integral is Part (a):-  ∭E z dV Here,  E= x, y, z :  0≤x≤2,   0≤y≤2,  0≤z≤3

Q: The linear DE.s is called homogeneous if R(x) is equal zero True O False O

A: True

Q: Evaluate the triple integral. SS. dV x² + z? E = {(x, y, z)| 1 <y< 4, y<z< 4, 0<x< z

A:

Q: The value of the triple integral (r + y)dzdydx

A: To evaluate  ∫01∫0x∫0x+y(x+y) dzdydx Formula used ∫dx=x∫xn dx= xn+1n+1∫abf1(x)= f(b)-f(a)

Q: (a) SII+y+z) dz dy dx

A: The given triple integral is: I=∫01∫01∫01 x2+y2+z2 dz dy dx

Q: - dx dz dy . x² +z? Evaluate the iterated triple integral

A: To evaluate the triple integral: ∫02∫0y∫0z3zx2+z2dx dz dy

Q: Evaluate the triple integral. 5xy dV, where E is bounded by the parabolic cylinders y = x² and x =…

A: The point of intersection of the cylinder x=y2 and y=x2 is 0 and 1.

Q: Evaluate the triple integral. SI. {(x, v, z) | 0 < y s 2, 0 < x < V4 - y?, 0 < z < 5y} 2x dV, where…

A:

Q: 3) Evalnate the iterated integral oy Cer the to palar corrdinate, 2x-x a) hny? dy dx

A: Introduction: Since you have asked multiple questions, we will solve the first question for you. If…

Q: The distance Cdlin meter of a moving body with respect to time (t) in hour is gruen in the below…

A:

Q: By making an appropriate change of variables, evaluate the double integral I = (x + y)e²²-y², dædy…

A:

Q: Evaluate the triple integral. {x, y, z) | 0 s y s 2, 0 sxs 4- y², 0 sz s Sy 6x dV, where E =

A: From the given problem:   ∫∫∫E6xdV   And region:   0≤y≤20≤x≤4-y20≤z≤5y   So, we can write as:…

Q: The double integral f(x)g(y)dydx ,where a,b.c, and C d are constants, is equal to

A:

Q: By using homogeneous meth od , solve dy %3D

A:

Q: The product of the triple integration (x² + y? +z*)i dzdydx pu Jasa gai استخدم الاحداثيات الكروية(

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.