Find the area of the region between the curve y = 3 - x2 and the line y = -1 by integrating with respect to a. x, b. y.

Q: Sketch the region R whose area is given by the double integral. 3 19 - y2 dx dy

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Q: Find the area of the region enclosed by the curves y = x and y = 4x by integrating with respect to…

A: The given curves are: y=x2  and   y=4x The region enclosed by these two curves is given as:

Q: Use an iterated integral to find the area of the region bounded by the graphs of the equations.

A: First we need to find the x coordinates of the points at which the graphs of the functions…

Q: Find the area of the region enclosed by the curves y = x2 and y = x + 2, integrating with respect to…

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Q: Find the area of the region by bounded by y = 4x and y = 2x – 4 by integrating with respect to y.…

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Q: Sketch the region of integration. rIn(x) f(x, y) dy dx

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Q: Determine the area of the region enclosed by y=√x+2y=x+2, x=−2x=-2, and y=2y=2. Round your limits of…

A: Given curves are, y=x+2 x=-2 y=2 Objective is to find the area of region enclosed by the given…

Q: Sketch the region of integration and evaluate the integral: 3y e*dxdy.

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Q: Find the area of the region bounded by y = e* – 1,y = lnx,y = 0 and y = 2, first integrate with…

A: Step 1 :              find area bounded by  y=ex-1…

Q: Find the region bounded by the curves y = x and y = x² using a dx integral.

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Q: Find the area bounded by the curves y= x', x = 2, and y = 0 using double integration.

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Q: Find the arca of the region bounded by y = e, the r-axis, and r > 0. You will need to evaluate an…

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Q: sketch the region of integration, reverse the order of integration, and evaluate the integral.

A: Given: ∫03∫x/31ey3dydx To Find: a. Sketch the region of integration.b. Reverse the order of…

Q: Find the area of region that is bounded by the given curves. Integrate with respect to x and then…

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Q: Find the area bounded by the curves y = x³, y = 1, and x = 0 using double integration.

A: Area of the required region is 3/4 see below the calculation

Q: Sketch the region D of integration, and then evaluate the integral by reversing the order of…

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Q: Find the area of the region enclosed by the curves y = x² and y = x by integrating with respect to…

A: Let f(x)=y=x2      (1)g(x)=y=x          Compare x=x2x2-x=0x(x-1)=0x=0 or x-1=0x=0 or x=1Put value of…

Q: Sketch the region whose area is given by the definite integral. 36 - x2 dx y y 12 35 30 25 20 15 10…

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Q: Sketch the region of integration. "In 10 r10 1 dy dx In y

A: As y varies from y = ex to y = 10 , we see that x varies from x = 0 to x = ln 10

Q: Find the area under curve y= (e*/x )dx from x=0 to x-4. use midpoint method with n=D4

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Q: Find the area bounded by the curve y = e^x , y = e^-x and x = 1, by integration.

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Q: Use an iterated integral to find the area of the region bounded by the graphs of the equations y =…

A: Consider the following equation of curves: y=x32y=2x Intersection points of curves:…

Q: Sketch the bounded region enclosed by y = e3, y = e't and x ,3x 7x =1. Decide whether to integrate…

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Q: Sketch the area bounded by x^2 + 2y = 4 and x + y + 2 = 0 on the image below and determine its area…

A: Sketch the bounded region.

Q: Find the area of the region by bounded by y = 4x and y = 2x – 4 by integrating with respect to y.…

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Q: Sketch the region of integration for the integral 1 dx dz dy. Y 0. Write the five other iterated…

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Q: sketch the region of integration and evaluate the integral.

A: Given, ∫0π∫0sinxydydxwe have to evaluate the integral and sketch the region of integration.

Q: Question included in image

A: The region of Integration can be defined as

Q: Identify the integral with Type I region between S 2ny dx dy and S 2ny dy dx g(y) g(x) and compute…

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Q: Sketch the region of integration and evaluate the integral || dx dy 1 y

A: The Given Integral is: ∫12∫yy2dx.dy

Q: Sketch the region of integration, reverse the order of integration, and evaluate the integral. 27 3…

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Q: How far is the centroid of the area boundded by the curves y=e^x, y=e^-x, and x=1 measured from the…

A: We have to find the distance of centre of mass from y Axis  So , find only x coordinate of centre of…

Q: Question included in image

A: Given:

Q: 1. Find the area of the shaded region by (a) integrating with respect to x and (b) integrating with…

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Q: Find the area bounded by the curves y = x3 , y = 1, and x = 0 using double integration.

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Q: Sketch the region whose area is given by the definite integral. 25 y 2 0.5 2.5 yA.5 y 2 2x

A: Let fx=2-x=2+x        -2≤x≤02-x          0≤x≤2 Now for -2≤x≤0 Graph of fx=2+x is a line segment with…

Q: sketch the region of integration, reverse the order of integration, and evaluate the integral.

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Q: /2-y² (г + у) dx dy. Jo Jy

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Q: The value of (4xy- (sinx)³)dx + (x² + y9)dy (Correct to ONE decimal place) where C is the region…

A: Let F=Px,yi+Qx,yj be the vector field and C be the boundary of the region D. To evaluate the given…

Q: Set up the definite integral that gives the area of the region. Y1 = x2 + 2x + 4 Y2 = 2x + 8 dx -2

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Q: Find the area of the region enclosed by the curves y = x² and y = 4x by integrating with respect to…

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Q: Find the area of the region by bounded by y 4x and y = 2x – 4 by integrating with respect to y. The…

A: given curve y2 =4x and y=2x-4

Q: Sketch the region enclosed by the given curves and decide whether to integrate with respect to x or…

A: This question can be solved using application of integrals to find area under curves.

Q: a) Find the area between the two curves y = 6 – x and y = x² by (i) integrating with respect to x…

A: Given curves: y=6-x and y=x2 To find: The area between the two curves y=6-x and y=x2 by…

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: Use an appropriate change of variable to evaluate the double integral: dA, y+x cos R where R is in…

A: As per our guidelines we are supposed to solve only one question. For the solution of the first…

Q: Use an iterated integral to find the area of the region bounded by the graphs of the equations y = 4…

A: Given: The region bounded by the graphs of the equations y=4-x2, y=x+2.

Q: Find area of the region bounded by x2 + y2 = 6?, 5y = -7x and 2ly = %3D 11x where y > 0. Leave your…

A: The region bounded by x2+y2=62, 5y=-7x & 21y=11x where y ≥0

Q: Sketch the region of integration. '7 [In(x) f(x, у) dy dx y

A:

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.