x³ – 6x2 + 8x, and y = x² – 4x - -

Q: find the area of the region that is enclosed between the curves y=x2+2x       y=x+2

A: The given curves are y = x2+2x and y = x+2.

Q: Find the area A of the region between y = 4x2 + 10 and y = 2x + 7 over the interval [-3, 2].

A:

Q: Find the area enclosed by the curves f(x) = 16x and g(x) =2x4

A: We need to find the area enclosed by the curves

Q: Find the area of the region bounded by 2x and the y-axis using the horizontal strip. 4 12 y² +1

A:

Q: Find the area bounded by the parabola x = y² + 2 and the line y = x – 8. 11 -2 3.

A: We have to find out the area bounded by the two curves

Q: Find the area within the curves y= 25- x', 256x=3y², and 16y = 9x².

A: as per the guideline i can solve only first question

Q: Find the area of the region bounded by the parabola  y2=4x and x2=4y

A:

Q: Find the area of the region enclosed by the curves y = x³ and y = 4x. 24 8 16

A:

Q: Determine the area enclosed by the curve 2x² + 2y² - 2x + 6y - 3 = 0

A:

Q: find the area bounded by axes and line 3x+2y=12

A:

Q: Find the area between the curves x² and 3x – 2

A:

Q: Find the area of the regions enclosed by the two curves, y =x +3 and y = 4x+8. %3D

A: From the given problem:   y=x2+3 & y=4x+8       Now finding a point of intersection:…

Q: Find the exact area enclosed by the curves, y=x5 - 6x3 + 4x and y = x.

A:

Q: Find the area of the regions enclosed by the two curves, y =x +3 and y = 4x+8.

A: Given that: y=x2+3           .............(1)y=4x+8           .................(2)

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

A: Here we have to find the area of the region between the curves y=x2+9 and y=10+2x over the interval…

Q: Find the area between the corves y= 2-x² and

A: Find the area between the two given curves First draw both the equations in a single plane To draw…

Q: Find the area of the region enclosed by the parabolas y x? and y = 2x – x². -

A: The area between any two curves f(x) & g(x) on an interval [a, b] is given by the formula:…

Q: Find the area of the region enclosed by the line y=4x and the curve y=x³ + 3x².

A:

Q: The area of region bounded by the parab y = 2x – 4 is

A: Introduction: Integration is a method of bringing separate parts to form a whole. We find a function…

Q: Find the area of the region between the line y = 2 - x and the x-axis, for 0 < x≤ 4.

A: In this question, the concept of integration is applied. Integration Integration is a method of…

Q: Find the area bounded by the given curves. y = 8x3 + 7 and y = 8x + 7 _________ square units

A:

Q: . Find the area of the region bounded by the curves y = 2x? - 8x + 12 and y = -2x+ 12.

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Find the area of the region enclosed between the curves defined by the equations y = x² – 2x + 2 and…

A: Solve the following

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

A:

Q: Find the area of the region enclosed by the line y = 4x and the curve y = x3 + 3x?

A: Given: y=4xy=x3+3x2

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

A:

Q: Find the area bounded by the given curves. v = 6x² – 16x – 7 and y = 3x2 + 2x – 22 | square units

A: Given curves are: y=6x2-16x-7y=3x2+2x-22

Q: 2. Find the area enclosed between the curves y =x² +2x +11 and y =-4x+2.

A:

Q: Find the area between the curves.  y = |9x|  ,  y= x^2 - 10

A: First we graph the functions. They cut at (-10,90) and (10,90)Area from x=-10 to x=0 is equal to the…

Q: Find the area lying between the parabola y = 4x – x² and the line y = x -

A:

Q: Find the area of the region bounded by the parabola f(x) = 16-x^2 and the lines  x=0 and x = 4 and…

A: Givenf(x) = 16-x2lines x=0, x=4 and x-axis(y=20)

Q: Find the area of the region enclosed by the curves y = 7 – 2x² and y = x² + 4

A: We need to find the area of the region enclosed by the curves y=7-2x2    and    y=x2+4. Let us plot…

Q: find the area of the portion of the cylinder x²+z²=16 lying inside the cylinder x²+y²=16

A:

Q: Find the area of the region bounded by the curves y = -x² – 3x + 4 and y = x2 – 3x – 4.

A: We first sketch the region using a graphing calculator y=-x2-3x+4 (violet) y=x2-3x-4 (black)

Q: Find the area of the region bounded by x = the horizontal strip. y²+1 and the y-axis using

A: Find the area of the region bounded by x= 1/(y2+1) and the y-axis using the horizontal strip.

Q: Find the area of the region enclosed by the line y=4x and the curve y= x3 + 3x2

A:

Q: Find the area enclosed by the line x=y and the parabola 4x+y² =12

A: Given:         The line x = y  and the parabola 4x + y2 = 12   To find:           The area…

Q: Find the area of the region bounded by y = x² - 5x + 6, the x axis, and the vertical lines x = 0 and…

A: Given that y = x2 - 5x + 6 ; y = 0 (x - axis) ; x = 0; x= 4  We have to find the area of the region…

Q: Find the area between the curves x2 and 6x – 5

A:

Q: Find the area of the region enclosed by the curves 4x² + y = 4 and x - y = 1.

A:

Q: Determine the area of the region bounded by y = 2.r2 + 10 and y = 4x + 16.

A: We sketch the region using a graphing calculator

Q: Find the area of the region enclosed by parabola y=3-x2 and the line  Y=3-2x

A: We have to find the area of the region enclosed by parabola y=3-x2 and the line y=3-2x. The point of…

Q: Find the area of the shaded region (using the area between two curves). y=x2 - 4 y=2x² •x - 6

A:

Q: Find the area of the region enclosed by t 4x² + y = 4 and x* - y = 1.

A: Here we have to find find the area enclosed by the region 4x2+y=4 ...............(1) and…

Q: Find the area of the region between the x-axis and the curve .3 y = x³- 4x - 2 < x<2 ?

A: Let us first plot the graph of y=x3-4x, -2≤x≤2.

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

A:

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

A:

Q: Find the area of the region bounded by the parabola y2 = 2x-2 and the line y = x-5 using (a)…

A: We will find out the required area.

Q: The area of the region bounded by the two curves y = x² and y = 9 is Square Units

A: Draw the both curve than find their intersection points and integrate in that interval.

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.