The region shown below is bounded by the curve y = 2x3 and the lines x = 8 and y = 3.

Q: The area of the region bounded by y = v9 – x² , the x-axis and the line y=x in the first quadrant…

A: The area between the curves y=9-x2, y=x, x=0 :The area between curves is the area between a curve fx…

Q: : Find the area of the region in the first quadrant that is bounded above by y x and below by the…

A: SOLUTION-

Q: 4. Find the area of the region in the first quadrant bounded on the left by the y-axis, below by the…

A:

Q: Find the area of the region between the line y = 2x and the curve y = x²+ x – 2

A: y=2x --------(1) y=x2+x-2 -------(2) For points of intersection…

Q: Find the area of the region in the first quadrant bounded on the left by the y-axis, below by the…

A: We have to find the area .

Q: Find b such that the line y = b divides the region bounded by the graphs of the y = 9 − |x| and y =…

A:

Q: Find the area of the region in the first quadrant that is bounded above by y = √x and below by the…

A: Now the diagrammatic representation of the area is,

Q: Find the total area of the region enclosed by the curve x = y^(2/3) and the lines x = y and y = -1.

A: To determine the area bounded by the curves.

Q: The area of the region enclosed by the curve 4x2+25y²=50 is:

A:

Q: Sketch the region enclosed by the given curves. 3 y = - y = 12x, y = x, x > 0

A: The sketch of the given region is:

Q: The area of the region bounded by the curves y=x and y= 20-x² is

A:

Q: 2. Find the area of the region bounded by the curve y = x^3 − 2x^2 − 5 x + 6, the x-axis, and the…

A: Given: y=x3-2x2-5x+6 For finding area of region bounded by given curve with x-axis and the lines…

Q: Sketch the region enclosed by the given curves. y- Vx- 3, x - y - 3

A: To find the area of enclosed region of the given curves, first we find the intersecting points of…

Q: Sketch the region bounded by the graph of the equations and find the area of the region. x = y² -…

A: Solution

Q: The area of the region bounded by the two curves y = x“ and y = 4 is

A:

Q: Find the area of the region bounded by the curve 2-4r and the lines x = 1 and x = 4.

A: To find the area

Q: 2. Find the length of curve of shaded region in the shape. y = x2 2.

A:

Q: Find the area of the region bounded by the curves y = x ^ 3 - 12x, y = x ^ 2.

A: y = x ^ 3 - 12x, y = x ^ 2.

Q: Sketch the region bounded by the given curves, then find its area. y = 12 - 3x^2, y = 4 - x^2

A:

Q: Find the area of the region between the line y=2x and the curve %3D y =x² +x-2.

A: Given:          y=2x and the curve y=x2+x−2

Q: Sketch the region bounded by the given curves, then find its area. y = 2x - x^2, y = 2x^2 - 4x

A:

Q: The area bounded by the curve z = y.y-axis and the lines Y3D0. y32 is s

A:

Q: The area of the region bounded by the two curves y = x² and y =4 is

A:

Q: The area of the region bounded by the curve y= x3−3x2−x+3 and y=0 is

A:

Q: Sketch the region enclosed by the given curves. 4x y = 1+ x2 4x2 y = 1+ x3 y

A: Given area can be given as below :

Q: Find the area bounded by the curve x = y² + 2y and the line  x = 3.

A:

Q: find the area of the region bounded by the parabola x=y^2+2 and the line y=x-8

A:

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

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 given curves. 1. y +4x = 0 and x+2=0

A:

Q: The region is bounded by the curve y = 6x – x² and y = x² – 2x –

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find the enclosed area by the curve with equation y=x^2-9 and x-axis in the region[-1,2]

A:

Q: Find the area of the region between the line y = 2x and the curve y = x2 + x − 2

A:

Q: Find the area of the region bounded by the two curves. y = x2 + 3 y = 7x + 3

A:

Q: Find the area of the region bounded by the curve y^2 = 4x and the lines x = 1 and x = 4.

A:

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

A:

Q: Find a such that the line x = a divides the region bounded by the graphs of the equations into two…

A: Given, y2=4-xx=0

Q: Find a such that the line x = a divides the region bounded by the graphs of the equations into two…

A: Given,    y = x,  y = 4  and  x = 0 So the region bounded by these curves is given by shaded region…

Q: Find the area of the region bounded by the three curves y = x², y = 8 - x², and 4x - y + 12 = 0.

A: Given: y=x2y=8−x24x−y+12=0

Q: Find the area of the region in the first quadrant bounded by the circle (x - 1)² + y² = 1, and the…

A:

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

A:

Q: The region bounded by the curves y=1-x^3. ,y=e^x.  And the line y=3

A:

Q: The region is bounded by the curve y = 6x – x² and y = x² – 2x – 10

A:

Q: Find the region bounded by y=2sqrt(x-1), the x-axis, the line x=5 and the line x=17.

A:

Q: 4. Find the area of the region bounded by the parabola x=y^2 +2 and the line y=x-8 *

A: Given curves are x=y2+2, y=x-8 We have to find the area bounded by this region.

Q: The region is bounded by the curve y = 4x – x², y = 4 and the y-axis.

A:

Q: Consider the region bounded by the curves y= X,y= 3-2x, and y=3 %3D

A: 1) Shaded the region :

Q: y=√x, x = 4, and the x-axis.

A: Consider the given function y=xand the x-axis

Q: Find the area of the region in the first quadrant bounded by the line y = 8x, the line x = 1, the…

A: Intersection Points are:  The line x=1 will intersect the x-axis at (1,0) because y is 0 at…

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.