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: Estimate the area under the line y= 2x+1 using six rectangles and right endponits over the interval…

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Q: 2. [L-4) 5 (y+3)*

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Q: 3x+1 2-2x+2

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Q: Compute line integral of F(x,y) = (2x² – 3,₁²³)^² + (2x +34²) ↑ с over the following C F-dr SCF ¾ ç…

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Q: Verify by integration that the Xbar location of the centroid of a quarter circle is (4r/3 pi)

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Q: Evaluate the integral ſſ /ydA, where T- triangle with vertices (1,0), (0, 1), (1, 1).

A: Let us consider the double integral  I=∫ab∫f(x)g(x) f(x,y) dydx    or I=∫ab∫f(y)g(y) f(x,y) dxdy…

Q: Evaluate the integral. 5x а. (25x²-10x +198)+c 125 Ob. (25x²+10x-202)+c 125 e -(25x²– 10x - 201)+ c…

A: The given integral is ∫x2-8e5xdx. Here we use the integration by parts formula:…

Q: Find the area between the curve y= 2x +10 and line y4x + 16 64 64/5 64/3 O 64/7

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Q: What is the integral of the function 2x + y over the bounded region formed by the curves * = = 2y²…

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Q: Find the area bounded by the curves x y = 8 (in green), y blue) and the line 3y sliced pizza? 2 =…

A: Let's find area of the sliced pizza.

Q: Find the area bounded by x=2y^2-4y+4 and x=y^2-2y+4.

A: To find the area between the curves x=2y2-4y+4, x=y2-2y+4.

Q: (4) Find the area of the region bounded by f(x) = 12 - 3x², the x- - and the lines x = 0, and x = =…

A: The region bounded by functions  , the x axis and the lines  and

Q: Find the area of the region bounded by y = x2+ 2x – 1, y =÷+x-÷, x = -3, x = 1.

A: Find your answer below

Q: (1,0) (1,0) = | (x? – y?) dx + 2x y dy + i| - 2x y dx + (x² – y²) dy (0,1) (0,1) 1- x? + y? = 1

A: In this, We calculate the value of the given integral and find the answer in a/b+ic/d form.here…

Q: Let R be the region in the first quadrant bounded by the graph of y = x² + 4x and the x-axis. A…

A: Step 1: Step 2: Step 3: Step 4:

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

A:

Q: Write a line integral(s) that would give you the area the graph of f(x,y)=x^2-3y^2-4x+6y+30 and the…

A: The line integral of  function F along with curve C is defined as  ∫CF·dr=∫C(M,N)·(dx,dy)=∫CM dx+ N…

Q: sy2-3x²+9 J. Tra St 2 Convert x - gy dzdydx to integral of cyclındri cal coordinatcs then evaluate

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Q: compute the area of the region determined by the vertices (-1,0), (0,1), (1,0) and (0,-1) using…

A: Given: Vertices are given as (-1,0), (0,1), (1,0) and (0,-1)  To find: Area of the region bounded by…

Q: Which integral corresponds to the area of the shaded region? The parabola is y = x? –1 while the…

A: Given query is to find the the integral for the area of shaded region.

Q: Find area of region x = 45 − 5y2,  x = 5y2 − 45

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Q: Write the integral that can be used to find the region bounded by x = -3y² + 4 and x = y³.

A: We have to construct  the integral to find the region bounded by given curves.

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.