Solve the integral. + yz )do; o: part of the plane x + y +== 6 that lies in the first octanct.

Q: the volume of the solid enclosed by the paraboloids z = = 16 (x? + y?) and z = 18 – 16 (x² + y²

A:

Q: Find the area of the paraboloid x? + y +z² = 2 by the plane y = 0.

A: We need to calculate the area of the paraboloid x2+y+z2=2 that is cut by the plane y=0. The equation…

Q: By making an appropriate change of variables, evaluate the double integral I = (z + y) e v drdy…

A:

Q: 1 in 1in y 1 in 3 in 1 in X

A: Consider the diagram and divide into four regions as shown below, Now, make a chart and evaluate…

Q: Find the volume generated by the equation x? + y² – 4x – 6y – 12 = 0 if it is rotated about the line…

A: The volume of the solid generated by resolution can be calculated by calculating the surface area of…

Q: Find the surface area of the portion of the paraboloid z = 9- r - y? between the cylinders r?+ y? =…

A:

Q: Find the surface area of the part of the plane 4+ 2x + 3y that lies inside the cylinder x² + y? 9.

A: The area is given by using double integral

Q: Use spherical coordinater to set up the integmal SzdV, the integral SSSz dV, where Q lies between…

A:

Q: FR,y-I, and x= | , a bout

A: Given that,

Q: Assume a to be a nonzero real no.. Determine the area of the portion of surface xy = az in the fir…

A:

Q: Determine by direct integration the centroid of the area shown in the figures. Where a= 22 cm and b=…

A: Given that  a=22cm. Also,   b=222mm=222×0.1cm=22.2cm   According to the figure, both curves…

Q: The value of the integral dz , over the Contour C |2 – 2| = 2 is equal 2Ti 2rie 2rie

A:

Q: Prove that the integral of the bottom of a half ellipsoid, (x/a)^2 + (y/b)^2 + (z/c)^2 =1, is equal…

A:

Q: Use a triple integral to find the volume of the solid shown in the fig z = 64 – x² – y? 20 60 50 40…

A:

Q: 6. Use Green's Theorem to show that the area of the unit disk x2 + y? <1 in R? is T by evaluating a…

A:

Q: Use Green's Theorem to evalute this integral where C is a triangle with point coordinates (0,0),…

A:

Q: By double integral, find the volume of the solid enclosed by a paraboloid x + 2y2 + z = 16, the…

A:

Q: Use the triple scalar product to find the volume of the parallelepiped having adjacent edges u = 4i…

A:

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

A:

Q: Calculate the area of the surface S. x2 that lies between z = 2 and z 6. S is the portion of the…

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

Q: The area of the surface p = 2, 0sz<5,0<¢< T is 201 Select one: O True O False

A:

Q: Evaluate the integral by changing to cylindrical coordinates: , N Sy xzdzdxdy x²+y²

A:

Q: Evaluate the given contour integral, where C is unit circle z=1. 3e cosz 2z +4 -57 + 2z- 4i 3 z' +…

A:

Q: If V=i +2j+3K, V,=zi +2j +2K, V = 3i+3 j +K, find the Volume?

A: Given vectors are V1→=i+2j+3kV2→=2i+2j+2kV3→=3i+3j+k So volume is V1→.V2→×V3→

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

A:

Q: If V=i+2j+3k, V,=zi +2j +2K, V = 3i+3 j +K, find the Volume?

A:

Q: Use geometry to evaluate ∫∫∫R 1 dV where R is the region inside the sphere x2+y2+z2=4.

A: Given R as the region inside the sphere

Q: Evaluate the integral /R 2xy dA, where R is the triangle 4x + y 0, y 2 0.

A:

Q: 1. Calculate the integral |- z+i dz throughout the contours C: z' + 2z? a.) |z +2-i|=2; b.) |z – 21|…

A:

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

A:

Q: SSx x dA; R is the portion of the disk x +y s 16 in the second quadrart

A: According to the given information, it is required to find the value of the given integral.

Q: Find the area of the part of the sphere r? + y + z² = 4 that lies within the first octant and inside…

A:

Q: Prove that dr-V3Ta? where こis the intersection of the plates: x²+ and and F=ly,Z,x)

A:

Q: Use spherical coordinates to evaluate the triple integral [[[ 2² + 3² + 2²dV, where E is the ball:…

A: We will first change it into spherical coordinate and then solve it.

Q: Use the change of variables formula to prove that the volume of the ellipsoid given by ()* + (#)* +…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the volume of the solid that lies under the elliptic paraboloid z = 3y? – a? + 4and above the…

A:

Q: Use Cauchy's Integral formula to evaluate the integral: Sa (z+1) e2z dz where C is a circle |z| = 3.…

A:

Q: Evaluate ffp(4xy + 1) dA, where R is the region in the upper half-plane bounded by the circles a? +…

A:

Q: Write an integral formula of the solid generated by revolving the region enclosed by the triangle…

A:

Q: Find the volumes of the solids

A: We have,

Q: I = dz . Jc (z – })²

A:

Q: Find the volume of the solid that lies under the elliptical paraboloid z = 2x2 + y? +4 and above the…

A: Given, z=2x2+y2+4 To find Volume of Solid

Q: x3 + axy? +1+ iv(x, y) dz |z|=1

A:

Q: Find the area of the part of the plane x + 4, y + z = 4 that lies in the first octant. 1. A = 12 2.…

A:

Q: If V=i +2j+3K, V,=2i +2j +2K, V = 3i+3 j +K, find the Volume?

A: We can find the volume using scalor triple product .

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: Determine the volume of the solid lying under the elliptic paraboloid z = 6y? – 2x2 + 3 and above…

A: To evaluate the integral

Q: If V=i +2j+3K , V=zi+2j+2K, V= 3i+3j +K, find the Volume?

A: Given→V1→=i+2j+3k,                V2→ =2j+2j+2k,                V3→=3j+3j+k      V1→V2→V3→=123222331…

Q: What is the value of the double integral 128(e – 1) e(42+8y)? dA, 2 R where Ris the triangular…

A:

Q: Evaluate the iterated integral. J. J, J vz dx dz dy A 45 в) 34 (© 47/3 D) 5

A: Topic = Integration