Sketch the region enclosed by the curves y = x2  and y=4x-x2 and find its area.

Q: Find the area of the region bounded by the curve y=1- and the x- axis.

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Q: Sketch the region bounded by the curves x = Vy + 3 , x =y+1 and evaluate the area

A: .

Q: Sketch the region enclosed by the given curves and find its area. y = v2x, y = a², 0< x < 6

A: The region is sketch is below:

Q: 31. y = x', y= 2 – |x|

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Q: Sketch the region enclosed by the curves and find its area. y = 7x ,y = 7Vx, x = - and x = 1 Enter…

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Q: Sketch the region bounded by the curves y = vx + 4 , y=x +2 and evaluate the area.

A: Given Curves are     y = x+4   and    y = x+2  first equation can also be written as  x = y2 -4 now…

Q: Sketch the region bounded by the curves x = Vy+ 8 , x = y – 4 and evaluate the area.

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Q: 1. y = a2, y = Va, = x2, y = Vr. on the interval 0.25, 1]

A: The objective is to find the area enclosed between two curves.

Q: Find the area of the region bounded by the curves y 5x, y 2x-3 in the first quadrant. %3D

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Q: Sketch the region enclosed by the curves à - 5 = 4y and x − 21 = (y — 4)², and compute its area.

A: x-5=4y⇒x=4y+5     x-21=(y-4)2 ⇒x=(y-4)2+21 Area between the curves…

Q: Sketch the region enclosed by the given curves andfind its area. y = x2 ,y = 4x - x2

A: Let us find the point of intersection by equating the two curves  x2=4x-x2 x2+x2-4x=0 2x2-4x=0…

Q: What is the area of the region enclosed by the curves y=e^x, y=x^2-1 and the lines x=-1 and x=1?

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Q: Sketch the region enclosed by the curves and find its area. 1 y = 9x² ,y = 9 Vx,x = - and x = 1…

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Q: Sketch the region bounded by the graphs of the equations y = x2 − 1, y = −x + 2, x = 0, x = 1 and…

A: Sketch the region bounded by the graphs of the equations y=x2-1,y=-x+2,x=0,x=1 as shown below.

Q: Sketch the region enclosed by the curves and find its area. y = 9r° ,y = 9/ñx = andx = 1 = 9Vã.x…

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Q: Find the area of the region enclosed by the curves x + y: = 0 and x + 2y = 1.

A: Let's find.

Q: Calculate the area of a region bounded by the curves =x and y= Vx

A: I am solving this in step 2

Q: Sketch the region bounded by the curves y = vx – 2 , y = x – 4 and evaluate the area

A: Solve by integration

Q: Find the area of the region bounded by the curves: y = 2x and y = x² – 4x

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Q: Sketch the region enclosed by the curves and find its area y = 2 – x² and y = x

A: the given curves are y=2-x2 and y=x. To find: the area of the region bounded by the given  curves.…

Q: Sketch the region enclosed by the curves x = y² + 2 and x 6 and find its area.

A: Given curve

Q: 2 y = 12 – 3x", y= 4 – x- — х |

A: Let's find.

Q: Find the area of the region bounded by the curves y = e", y = x e", and x = 0.

A: Given curves are y=ex, y=xex Point of intersection of the curves are evaluated as follows.…

Q: Sketch the region enclosed by the curves and find its area. y = x, y = 3x, y = -x + 4

A: Given; y=x, y=3x, y=-x+4   Now find the point of intersection between the line y=-x+4 &amp; y=3x.…

Q: Sketch the region enclosed by the curves y = - 1+x2 and y = 5 – |x|. Find its area.

A: given curves are                                        y=-31+x2 and y=5-|x|

Q: Sketch the region enclosed by the curves and find its area. y = x, y= 4x, y= -x + 4 AREA

A: Topic:- application of integration

Q: Sketch the region enclosed by the curves and find its area. 1 Y = V1 – 9x2' y = 2

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Q: Sketch the region enclosed by the curves and find its area. y = x, y = 2x, y= -x + 4 AREA =

A: The region is bounded by y=x, y=2x, y=-x+4

Q: sketch the region enclosed by the curves y=x^2 , and x=y-3 , and then find its area

A: Given: y=x2  and x=y-3

Q: Sketch the region enclosed by the curves and find its area. y = cos 10x, y = 0, x = 20' 10

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Q: Find the area of the region bounded by the curves y x2 and y = rVr + 2.

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Q: What is the area of the region enclosed by the curve y=e^x and the lines x=-1 and y=3?

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Q: Find the area of the region enclosed by the curves x=9y², x = 0, and y = 1.

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Q: ) Sketch the region enclosed by the given curves and find its area. y = -x² +4x, y=x² – 2x

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Q: Sketch the region enclosed by the straight line y = 4x − 4 and the curve y = x2 and find the area of…

A: Given, straight line y=4x-4  and the curve y=x2we have to sketch the region enclosed by given…

Q: Sketch the region enclosed by the curves and find its area. Enter the exact answer. Area = y = 2x²y…

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Q: Find the area of the region bounded by the curves y=−3x, y=√x  and y=6

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Q: Find the area of the region enclosed by the curves between their intersections. y = 4x2 and y = Vx

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Q: Find the area of the region bounded by the curves x = y + 3 and y = x – 1

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Q: Find the area of the region in the first quadrant that is enclosed by the curves x=y, y=x-, and the…

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Q: find the area of the region enclosed by the curves y = sinx, y = cosx, x = 0, and x = 2π

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Q: Sketch the region and find the area of the region bounded by y = 3x + 1, the lines x = 1 and x = 4,…

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Q: Find the area of the region bounded by the curves y = 6 – x² and y = x+ 4.

A: intersection  6-x2=x+4x2+x-2=0x2+2x-x-2=0x(x+2)-1(x+2)=0(x+2)(x-1)=0x+2=0 or x-1=0x=-2 or x=1⇒-2≤x≤1

Q: Find the area of the region enclosed by the curves: y = x' – 2x², y = 2x² – 3x

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Q: Sketch the region enclosed by the curves and find its area. y = |x – 2|, x – 5y + 10 = 0

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Q: Find the area of the region enclosed by the curves: y =x', and y= 2x-x

A: Consider the curves  y=x2y=2x−x2

Q: Find the area of the region enclosed by the two curves y = 2|x| and y = x² – 3.

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Q: Sketch the region enclosed by the curves y = xe¬x², Find the area enclosed by the given curves. `, y…

A: Given: y=xe-x2, y=x+1, x=2 for finding area enclosed by given curve and y-axis, first we draw region…

Q: Find the area of the region between the curves y=|x| and y=x^2-2

A: Proceed as shown...

Q: Find the area of region enclosed by the two curves y = Vx +1 and y = v2 x

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.