Find the integral of f (x, y, z) = 6 z z + 3 over the region inside the cylinder 9 and between -* - 5 y – z = -17 and - – 5 y + z = 17.

Q: Express the area of the region bounded by the given line(s) and/or curve(s) as an iterated double…

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Q: Express integral I y + x (-4x-2y) -0,x= 1 and y=0,y-1-xto T. of u- dydx in terms of (u)and (v) given…

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Q: The area bounded by y=3Vx and 2y =3x is revolved about the x-axis. Using cylindrical shell method,…

A: Consider

Q: use a double integral to find the volume of the indicated solid.

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Q: Find the volume bounded by z = 9-x²-y² and z = 0.

A: find explanation below

Q: write the triple integral for integrating f(x,y,z) over the region in the first octant bounded above…

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Q: Consider the region formed by the graphs of f (x)=sqrt( x) , f (x)= 1/x and x = 2. Set up the…

A: We sketch the region using a graphing calculator.  Red curve is : y=1/x Violet curve is: y=sqrt(x)…

Q: Use a triple integral to find the volume of the solid bounded by the graphs of the equations. 2- 2xy…

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Q: Find the volume of the solid generated by revolving the area bounded by x² - 2kx - 2ky + k² = 0 and…

A: To calculate the volume of the solid obtained by rotating the region bounded by the curves y=fx and…

Q: Set up a double integral that gives the volume of the region bounded by the two paraboloids z = x2 +…

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Q: Let R be the shaded region bounded by the parabola y = 4 - x², and the lines y = 1- 2x and y= -1, as…

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Q: Consider the region formed by the graphs of f (x)=sqrt (x) , f (x)= 1/x and x=2. Which integral…

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Q: 1) Use a double integral to find the area of the region enclosed by y= x² and y = 2x.

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Q: Use the double integral to compute the area of region bounded by: 1) y = x² , x = y²

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Q: 5.) Find the volume of the solid in the first octant bounded by 2x + 3y + 4z = 12 and the coordinate…

A: Above question is solved.

Q: Set up an integral for the volume of the region bounded by y = x², z = -1, x-y +2 = 0, and z = x2 +…

A: Given  Region bounded by y=x2             (1)z=-1           (2)x-y+2=0    (3)z=x2+2y2+3     (4)

Q: Express the area of the region bounded by the given line(s) and/or curve(s) as an iterated double…

A:

Q: Consider the region between the graphs of f(x) = 5 – x and g(x) = 2x on [1,4]. For each line of…

A: Note: According to the guidelines only one question will be answered please upload other questions…

Q: II. SET UP an iterated double integral that will give the volume of the solid bounded by 3x + 2y +…

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Q: set up 2 integrals in both the shell and washer method to compute the area between x-axis and y=x2…

A: Draw the curve, as follows:

Q: Find the area of the region using a double integral.  The region bounded by y = 5x^6 , 5x + y = 10,…

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Q: Find the centroid of the region bounded by y = 28x and y = 56 (x – 14). Enter the exact answer as a…

A: Given: The regions bounded by y2 = 28x  and y2 = 56(x-14). To determine: The Centroid of the region…

Q: Use a double integral to determine the volume of the solid that is bounded by z = 8-x² - y and z =…

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Q: 7. Use a double integral to find the volume under the surface z = xx² +y and over the rectangle R =…

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Q: The area bounded by y=3Vx and 2y =3x is revolved about the y-axis. Using circular ring method, set…

A: This question can be solved using the concept of circular ring method.

Q: Suppose that f(x, y) = 2x + 3y and the region D is given by {(x, y) | −1≤ x ≤ 5, − 1 ≤ y ≤ 5}. D…

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Q: 5. Set up an iterated triple integral in the order dxdzdy that gives the volume of the solid in the…

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Q: If the region under the graph of +++/-/1 -- y = x² + from x = 1 to x = 5 is rotated about the…

A: NOTE: Refresh your page if you can't see any equations. . the given function is  and the given…

Q: ZA So ydz + zdy+ ædz (3,4, 5) C , C2 (2,0,0) y (3,4,0)

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Q: Calculate the double integral in a general region where z = 2y bounded by x = x²+1 0, x= 1, y = 0, y…

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Q: Q1: By using the double integral determine the area that enclosed by the planes z = 0,x= 0, = 0. y =…

A: Using double integral.

Q: Sketch the region R whose area is given by the iterated integral. 8 (64 - y2 dx dy 60 8. 50- 6- y 4…

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Q: Suppose that f(x, y) = 5x + 3y and the region D is given by {(x, y) | - 3 < x < 3, – 3 < y < 3}. D…

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Q: Use the Midpoint Rule for the triple integral to estimate the value of the integral. Divide B into…

A: Solution  :

Q: What is the integral of f (x, y, z) = 5 x y+ 5 z over the region bounded by –12 z + 28 y + 19 z =…

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Q: У Consider the plate bounded by y = r3 + x2 + 2, = 12-3, = -1 and x = 1 as shown on the right Set…

A: Consider the given curves.

Q: Find the integral of xy over the region bounded by the x axis, the line y=x and the line x=1

A: For finding the limits , graph of the bounded region is to be determine.

Q: Find the abscissa of the centroid of the region between the parabola y = 6 − x2 and the line y = 1 −…

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Q: 1) z = 2 – x² – 2y², z = 1

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Q: What is the integral of f (x, y, z) = 4 y2 + 5 y z over the region bounded by –12 x +8 y – 2 z= -38,…

A: We will find out the required value of integral.

Q: Use an iterated integral to find the area of the region bounded by 2x - 5y = 0, x+y=6, y = 0.

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Q: The area bounded by y=3Vx and 2y=3x is revolved about the y-axis. Using circular ring method, set up…

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Q: Find by double integration the area of the region in xy, plane bounded by the curves y = x2 and y =…

A: Using vertical strip

Q: Evaluate the lino integral y+ + (4+2-x>y +2が Where C consitts of line segments from 0,-,2) to…

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Q: Sketch and set up the integrals for volume of the region bounded by y = x^2 + x - 2 and y = 3x + 13,…

A: Given are the curves  y=x2+x-2 and y=3x+13 We need to set up the integral for the volume of the…

Q: The area bounded by y=3Vx and 2y=3x is revolved about the y-axis. Using circular ring method, set up…

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Q: 3 4

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Q: Use residue to evaluate the Cauchy principal value of the improper integral 4z2 + 8 z4 + 13z2 + 36…

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Q: Use an iterated integral to find the area of the region bounded by the graphs of the equations  2x −…

A: 2x-3y=0,x+y=5,y=0

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.