Sketch the graph of the given curves and find the area of the region bounded on the left by the curve y=vx and bounded on the right by the curve x = 3 – 2y².

Q: find the area of the region bounded above by the curve y = 2e^-x + x, below by the curve y = e^x/2,…

A: To find the area of the region bounded above by the curve y=2e-x+x, below by the curve y=ex2 on the…

Q: Find the area of the region bounded by the parabola y = x 2  ,the tangent line to this parabola at…

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Q: Find the area of a region bounded by the curves y=e^(2x) - x^3 , the y-axis and x=1

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Q: Find the area bounded by the curves y2 = 4x 4х + у — 6 %3 0

A: We need to find the area bounded by the curves y2=4x4x+y-6=0

Q: Find the area of the region bounded by the curve y = xe and the raxis from x- 0 to x =3 0.5 -0.5

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Q: Find the area between the curves y = x²(x – 3) and y² + 8y – 16x + 48 = 0

A: Formula: The area between the curves on the interval given by, Given:

Q: Find the area bounded by the curve ay = x² and the lines y = a and y = 4a.

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Q: Find the area of the region bounded by the curves y = e* y² = 4x - 4 between y = 1 and y = 2. and

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Q: Find the area bounded by the curves x² = 4y + 4 and the line y =x + 2.

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Q: Find the area bounded by the given curves. 1. x^2=4y , 3x-4y+4=0

A: The area between the curves is the area between a curve fx and a curve gx on an interval a,b given…

Q: Find the exact area of the region that lies under the curve given by y = 10/2x +1, 0<x <1 %3D

A: We know the area of the region that lies under the curve  y=f(x),  a≤x≤b is given by Area =∫aby dx…

Q: Find the area of the region bounded by the given curves: y = x² y = 4x – 22

A: Given: y=x2, y=4x-x2 For finding area of region bounded by given curves, we draw graph of both…

Q: y = e²x and x - 2y + 5 = 0

A: x-2y+5=02y=x+5y=x+52The equations are: y=x+52y=e2x

Q: y2 = 4 – x and y² + y = x + 2

A:

Q: Find the area of the curve y = x° – 2x – 3 between x =- 1 to x = 3.

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Q: Calculate the area of the region bounded by the two curves y = x 2 and y = 4 using the formula A = i…

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Q: Find the area of the region bounded by the given curves. y = 1- 2 x2, y =|x|

A: Given: y=1-2x2y=x To Find: Area of the region bounded by the given curves.

Q: Find the area of the region between the curves y = x² +9 and y interval [-1,3]. = 10 + 2x over the

A: Given that:                      y=x2+9y=10+2xBetween [-1, 3]   NOTE: As per our answering…

Q: Find the area of the region bounded by the curve y=x^2−1 and the line y=15.

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Q: Find the area of the region bounded by the given curves. y = √x,  y= -3√x.  y= x- 2

A: It is given,Function 1: y= -3x1  OR x1 = y29                        (1)Function 2: y= x2- 2   OR x2…

Q: y = e²x and x - 2y + 5 = 0

A: I am attaching image so that you understand each and every step.

Q: Find the area of the region bounded by the curves y = y = -x² + 4x. 9/4 11/3 12/15 8/3 none of the…

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Q: Find the area of the region bounded by the curve y2-4r and the lines x = 1 and x = 4.

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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: Find the area between the curves y = x²(x – 3) and y² + 8y – 16x + 48 = 0 -

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Q: Find the area bounded by the curve x2 + y2+4x-14y +44 0

A: Topic:- area of circle  Note:- as per our guideline if more than one question uploaded than only…

Q: Find the area between the curves: y2=x x2– 2x + 3y = 2

A: we have to find the area between the curves :

Q: Find the area bounded by the two curves f(x) = x² – 8x + 8 and g(x) = - 2² + 6x – 8, and the two…

A: To find Area between two curves:  f(x)=x2-8x+8 and g(x)=-x2+6x-8 and two vertical lines x=3 and x=4.…

Q: Find the area between the curves x=y² –1 and x = 2y² – 2.

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Q: 2 y = x - 3x, y=x 3r.

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Q: I+y = 0, x = y2 +3g

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Q: Find the area bounded by the curve y = 7x In(x), the x-axis, and the lines x = 1 and x = e.

A: Given:y=7xlnxlines x=1 and x=eTo find:Area A=??

Q: Find the area of the region bounded by the given curves. y = sin n y = x² – 6x

A: The given curves are y=sinπx6, y=x2-6x. Find the area of the bounded region.

Q: 1. Find the area of the region bounded by the curves y = 3x and y=x².

A: Given : The curves y=3x and y=x2. The objective is to find the area of the region bounded by the…

Q: Find the area of the region R enclosed by the curves y = x2 – 2x and the х — ахis.

A: Given: y=x2-2x

Q: Find the area of the region bounded by the given curves. y= x2, y = 4x - x2

A: The given curves are,   y= x2,  y = 4x - x2

Q: Find the area of region bounded by the curves x= 2y+6 and x y-1.

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Q: y² = x y = x³

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Q: Find the area of the region enclosed by the given curves  y = 1/4x^2 y = 2x  x+y = 3 while x is…

A: I have done solution step by step in detail...go through the solution

Q: Find the area of the region between the curves x=((y-2)^2)/3 and y=8-x shown in the following…

A: Explained below

Q: 3. Find the area of the region between the curves y = Vx and y =x2.

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Q: Find the area of the region bounded by the given curve: r = 5e 4 on the interval 5

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Q: Find the area of the region bounded by the curves y² - 4x = 5 and 4x + 3y = −1

A: We can find the area of the region between the two curves using the double integration method. We…

Q: Find the area of the region bounded by the given curve: r = 5e° 6. on the interval 5"

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Q: Sketch the region bounded by the curve 8xe¯ª, the x-axis, and x = 2, and find the area of the…

A: To sketch and find the area of the region.

Q: Find the area bounded by the curves x2 = 4y + 4 and the line y = x + 2.

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Q: Find the area of the region that lies above the x-axis, below the curve x=t2+5t+8, y=e-t with 0≤t≤1.

A: Given that, x=t2+5t+8 y=e-t Where 0≤t≤1

Q: Find the area bounded by the curve x^2=4y+4 and the line y=x+2

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

A: Proceed as shown...

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.