Use double integration to calculate the area of the region 2 encolsed ye and x+y=2.

Q: Find the area of the region bounded by y = 10x , y = -9x, y = 4 and y = -8 using double integral.…

A: Explanation of the answer is as follows

Q: Use integration to find the area of the figure having the given vertices. (0, 0), (1, 4), (3, −2),…

A: We have to find the area using integration bounded by the points 0,0 , 1,4 , 3,-2 , 1,-3

Q: Shade the area of the region bounded by, x² + y? p Hence, find the area of the specified region…

A: we use integration to find area between curves

Q: Lnx y = y = xLnx 4.x

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Q: Use integration to find the area of the figure having the given vertices . (0, 2), (4, 2), (0, −2),…

A: Given vertices are (0, 2), (4, 2), (0, −2), (−4, −2).

Q: Shade the area of the region bounded by, x² + y2 < 7² and |x| + |y| 2 7 Hence, find the area of the…

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Q: Use integration to find the area of the triangular region having the given vertices. (0, 0), (8, 0),…

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Q: Solve by integration: A region is bounded between x=0, y=1, x=1, and y=(x-1)^2+1. What is the…

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Q: Find the area of the region bounded by y = ex and y = 12 − ex and the y-axis.

A: Given, y=exy=12-ex and the y-axis   Find the area bounded by the region:

Q: Shade the area of the region bounded by, x² +y? p Hence, find the area of the specified region…

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Q: Use integration to find the area of the region between y = x² + • the x-axis, x = 1 and x = 3.

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Q: find the area of the region enclosed by the curves y = 3x, y = -3 and y = 4 – x using integration.

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Q: Calculate the area of the region bounded by y= Vx+1 and y = x – 2x – 3. %3D

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Q: Use integration to find the area of the figure having the given vertices (0, 0), (1, 2), (3, −2),…

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Q: Sketch the region enclosed by x + y² = 30 and x + y = 0. Decide whether to integrate with respect to…

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Q: Sketch the region of integration and find the area of the region cut from the first quadrant by the…

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Q: Find the area of the region bounded by y = 2x , y = -8x and y = 2 %3D using double integral. Leave…

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Q: Shade the area of the region bounded by, x2 +y2sp2 and |x| + |y| 2p Hence, find the area of the…

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Q: Sketch the region enclosed by y = 4x and y 2x²!. Decide whether to integrate with respect to xlor y,…

A: In this question we have to find area of the region.

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: By double integration, Find the area between the line y=6-2x, the x-axis and y-axis.

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Q: Sketch the region enclosed by x+y2=42 and x+y=0. Decide whether to integrate with respect to x or y.…

A: The given curves are x+y2=42 and x+y=0 We have to sketch the region enclosed by these two curves and…

Q: Sketch the region enclosed by y=2x and y=6x^2 Use an integral to calculate the area of this…

A: Given : y = 2x y = 6x2    NOTE :- If two functions f(x) and g(x)g are plotted on a plane, for the…

Q: Decide whether to integrate with respect to x or y. Find the area of the region.   6x+y2=16,   x=y

A: here we have a y2 term so we will  integrate with respect to y the first equation is 6x+y2=16…

Q: Determine the area of the region bounded by y = xe¯x² , y = x + 1,x = 1, and the y-axis. %3D

A: Given  y=xe-x2y=x+1x=1x=0  i.e. y axis

Q: A projectile fired downward from a height of 112 ft reaches the ground 2 seconds. What is the…

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Q: Sketch the region enclosed by y=3x and y=2x^2. Decide whether to integrate with respect to xx or yy.…

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Q: Find the area of the region bounded by y = x* +1 and y = 3x – 1. %3D %3D

A: Since you have asked multiple questions, we will answer the first one for you. If you want any…

Q: Use integration to find the area of the triangular region having the given vertices. (0, 0), (8, 0),…

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Q: y = ; y = -x², x = 1, x = 2

A: Area between curves

Q: Find the area of the region bounded by y = 4x + 9, y = -6x + 9 and x = 14. Leave your answer correct…

A: Area of region bounded by given curves are evaluated.

Q: Evaluate the area of the region bounded by x=y^2 and y^2 = 6-x, using double integral

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Q: Shade the area of the region bounded by, x2 + y? p Hence, find the area of the specified region…

A: Given problem is :

Q: Find the area of the region bounded by the graphs of the equations y = x² and y = vx.

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Q: Solve by integration: What is the area of the region enclosed by the curve y=x^2 and the lines…

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Q: Sketch the graph of the curve y = (x – 7)(x – 7 – 1)(x – 7 – 2) Shade the area of the region bounded…

A: In the graph, the horizontal axis is x-axis and the vertical axis is y-axis. We need to find the…

Q: Find the area of the region bounded by x = 4- y and y = x– 2.

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Q: Find the area bounded by y=2x-x^2 , the x – axis, and the lines x =0 and x= 4.

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Q: Find the area of the region bounded by y = x² – x ,x = 2 , and x & y- axes

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Q: | = x – 2 and y =

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Q: Determine the area of the region bounded by y = xvx2 + 1, y = 1 e 2x, x = -3 and the y-axis.

A: First draw the region defined by these curves. If the region is bounded, then use the area under the…

Q: Sketch the region enclosed by x + y² = 20 and x + y = 0. Decide whether to integrate with respect to…

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Q: Find the area of the region bounded by x = 2y – y² and x = -y.

A: NOTE: Refresh your page if you can't see any equations. .

Q: Sketch the region enclose by y=x2-9x+21 and y = -x2+11x-27. Decide whether to integrate with respect…

A: Given data is : y=x2-9x+21 and y=-x2+11x-27  To sketch the region.

Q: Find the area of the region bounded by y=-x^2+3x+1 and y=-x+1

A: Please see the diagram below to understand what's going on:

Q: 4) Sketch the region and find the area bounded by + = 1, y = ±3 and y = x + 4 using double…

A: We have to find the area of the region.

Q: Sketch the region enclosed by y=4x and y=2x^2. Decide whether to integrate with respect to x or y,…

A: The equation of curves are : y=4x and y=2x2

Q: Sketch the region enclosed by y = 4x and y= 6x². Decide whether to integrate with respect to x or y.…

A: Given query is to find area under the curve.

Q: Sketch the region R of integration and switch the order of integration. 25 - x2 f(x, y) dy dx y

A: NOTE: Refresh your page if you can't see any equations. . the limit of y is  and the limit of x is…

Q: Sketch the region enclosed by x+y^2=6 and x+y=0. Decide whether to integrate with respect to x or y,…

A: We first graph the given equations. They intersect at (-3,3) and (2,-2)

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.