Find the area of the region in the first quadrant bounded by the line y=2​x x=4​ y=2/x and the​ x-axis.

Q: Find the area of the region between y = x sinx and y = x for 0 ≤ x ≤ π/2.

A: We need to Find the area of the region between y = x sinx and y = x for 0 ≤ x ≤ π/2.

Q: Find the area of the region between the curve y 4 In x and the horizontal axis for

A: We have to find the area of the region between the curve  y=4 ln x and the horizontal axis for…

Q: Find the area of the region bounded by the curves.  y = x(x2 - 1) and the x-axis

A: Given curves are, y=x(x2-1)and the x-axis y=0 .   First, find the intersection points:…

Q: What is the area of the region enclosed by the curve y=x(x-1) (x-2) and the x-axis?

A: Given:            Curve: y=xx-1x-2             Area =∫01xx-1x-2 dx+-1∫12xx-1x-2 dx…

Q: Find the area of the region bounded by the curves.  y = 8x2 and y = 1x

A: To find: The area of the region between the curve y=8x2 and y=x. Formula used: The area between the…

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

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 bounded by y=x^2, the x-axis and the line x=2.

A:

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

A:

Q: Find the area of the region bounded by the curves y= 2² - 3 and y = 2x + 5.

A:

Q: Find the area of the curve bounded by the curves y=x* and y=3x+4.

A: We have to find th: e area of the curve bounded by the curves y=x4 and y=3x2+4.…

Q: Find the area of the region between the curves 4x + y^2 = 12 and x =y.

A: 4x+y2=12    and  x=y

Q: Find the area in the first quadrant bounded by the curve y = 3x – x, the lines x = y = 2. 0 and

A: To find the area of the region bounded by the curve we use the formula Area=∫abf(x)-g(x)…

Q: FIND THE AREA OF THE REGION IN THE FIRST QUADRANT THAT IS BOUNDED ABOVE BY y=sqrt(x) AND BELOW BY…

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

A:

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?

A:

Q: Find the area of the region that lies between the curves y = x^2 and y =sqrt(x) from x = 0 to x = 4.

A: Given:

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

A: We have to find the area

Q: Find the area bounded by the pair of curves. y = x² + 4x and y = 4x + 1 square units

A:

Q: Find the area between the two Curves- y=x, a°y = x³ 3,

A:

Q: Find the area of the propeller-shaped region enclosed by the curve x - y3 = 0 and the line x - y =…

A: x-y3=0  &  x-y=0⇒y3=x  &  y=x⇒y=x13  &  y=x Now the diagrammatic representation of the…

Q: Find the area bounded by the curve y = 4x - x² and and the lines x = 0 and y = 4. %3D Answer:

A: we can find the area between the curve and the lines by integrating the curve function through lines…

Q: Find the area of the region that is enclosed between the curves y = x² and y = x + 6.

A: The given curves are, y=x2 and y=x+6. The objective is to find the area of the region that is…

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

A:

Q: 2 y = 12 – 3x", y= 4 – x- — х |

A: Let's find.

Q: Find the area of the region bounded by y = 9x + 8, y = -3x + 4 and x = 14. Leave your %3D answer…

A: Area between curves

Q: Find the area of the region enclosed by the line x = 2y and the curve x = y3 - y?

A: To calculate the area of the region bounded by the curves x=fy and x=gy, use the formula…

Q: Find the area of the region in the first quadrant bounded by the line y = x, the line x = 2, the…

A: the area of the region in the first quadrant bounded by the line y = x, the line x = 2, the curve y…

Q: Find the area of the region between the line y = −x and the curve y = x2 + x − 3

A: Area of the region is 32/3

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

A: The given curve is y2=4x and lines x=2 and x=4. From the given information,

Q: Find the area of the region bounded by y = 4x + 9, y = -6x + 9 and x = 14. Leave your answer correct…

A: Area of region bounded by given curves are evaluated.

Q: Find the distance of the centerof gravity of the area on the first quadrant region bounded by the…

A:

Q: Find the area of the region between the curves y |Jx and y x2-2 | Area between curves

A: Given,

Q: Find the area of the region between the curves 4x + y = 12 and x = y. Area between curves

A: Solution

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

A:

Q: Find the area enclosed between the two curves y=4-x^2 and y=x^2-2x.

A:

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

A:

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

A:

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

A:

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

A: Given data: The given equation of the line is y=x/4. The first equation of the curve is y=1+x1/2.…

Q: Find the area of the region bounded by the curves y = x 2 − 3x + 5 and y = 3x + 5.

A:

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

A:

Q: Find the area of the region between the curves 4x + y = 12 and x = y. Area between curves =

A: R

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

A:

Q: Find the area of the region in the second quadrant bounded by y= -x and y=x^4

A:

Q: Find the area of the region between the curves y = x² and y = x. Area between curves =

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Find the area of the region in the first quadrant that is bounded by y= \x , x- axis and y=x-2.

A:

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 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.