2. Find the area in the second quadrant bounded by the curve y = x' +4x² –x-4 and the x- axis.

Q: 2. Find the area in the third quadrant bounded by the curve x= y2 + 2y.

A:

Q: Find the area between (bounded) by the Curves y=x² +10x and y= 2x + 9°

A:

Q: y = ln x and x - y -4 = 0

A: Explanation of the answer is as follows

Q: 6. Find the area bounded by the curve 2y² + 4x + y = 0 and the line y = 2x.

A:

Q: 3. Find the area bounded by the curves x2 + y2 = 9 and 4x2 + 9y² 36, on the first quadrant.

A:

Q: Find the area between the curve y = 6x – 2x and the x-axis between x 1, and x = 3. ||

A:

Q: Find the area between the curve y=x^3 and its tangent through (1,1)

A: The slope of the tangent is given by y' at (x,y)=(1,1) y'=3x2At x=1y'=3 Equation of tangent line is…

Q: Find the area bounded by the curve y = 62xe-62x and the x axis from x =0 to x = 4

A: Area bounded by the curve y=f(x) and x-axis from x=a to b is given as, ∫abf(x)dx Some common…

Q: . Find the area bounded between the curves 5x-y x2 and y = 3x + x²

A: We have the given the curves y=5x-x2 and y=3x+x2 We have to find the area bounded by this two given…

Q: 2. Find the area between the curve y=-x and y+x²= 2x.

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

Q: Determine the area bounded by the curves y = -x² – 18x + 63 and y = (x – 3)². |

A:

Q: 4. Find the area bounded by the curves y = 2x – x2 and the x-axis

A:

Q: 16. Find the area bounded by the curve y=-x³--x²+3x and the line y=x. 16 4

A: 16)Given,y=x316-3x24+3x and y=x

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

A:

Q: find the area between the curves 2x^2+4x+y=0 and y=2x

A: Given that: 2x2+4x+y=0    and   y=2x

Q: 3. Find the area bounded by the curves x2 + y = 0 and 2x + y + 3 = 0.

A:

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

A: Given curves are  y2=4x, 2x+y=4 The region bounded by the above curves  is the yellow colored region…

Q: Calculate the area enclosed between the x-axis and the curve y = x2 - 1 between x = -2 and x = 2.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the area bounded by the curve y2 = 4x and the line 2x + y = 4 and provide a correct and…

A:

Q: Find the area between the curve  y = x2 + 3x + 2  and the x-axis from  x = −1 to x = 1.

A: We have to find the area between the curve y=x2+3x+2 and the x-axis from x=-1 to x=1.

Q: Find the area bounded by the curve 2x2 + 4x + y – 0 and the line y + x = 0

A: To find the area of region bounded by the given curves.

Q: 7. Find the area bounded by the curve y = 4x - x^2 and the lines x = 0 and y = 4.

A:

Q: Find the area bounded by the curve y (x- 2)(x + 1)(2x – 1) and x-axis.

A: We use integration to find the area.

Q: Find the area between the curve y = sin 2x and y = x^2

A: the area is 4/5

Q: Find the area between the two curves y = x^2 and y = 2x – x^2

A: Given:     To determine: The area between the two curves.

Q: Find the area between the curve y = x – and y = -x + 10x2 – 24x 10x + 24x

A:

Q: Find the area bounded by the curve y = 3x – x3 and the line y = 2

A: Given: y= 3x-x3; y=2 If f(x)> g(x) in the interval x=a to x=b, then the area between two curves…

Q: Find the area between x-axis and the curve defined by   y=2·x2−6·x on the interval [0‍,4].

A:

Q: 2. Find the area in the first quadrant bounded by the curve y = 3x – x³, the lines x = 0 and y = 2.

A: Given- y=3x-x3 To Find- The area in the first quadrant bounded by the above curve, the lines x=0 and…

Q: What is the area bounded by the curve y^2 = x and the line x - 4 = 0?

A: We have to determine area of bounded

Q: Calculate the area between the curves y = 7- 2x2, y = x2 + 4, and the x-axis.

A:

Q: 8. Find the area between the curves y = x x² and y = x2 – 4x between x = O and x = 2.

A: For calculating the area between curves first of all we will draw the schematic diagram of the…

Q: 22) Find the area of the region between the curve y = 2x/(1 + x2) and the interval -2 sxs2 of the…

A:

Q: 2. Find the area between the curve y = x3 – 6x2 + 8x and the x-axis.

A:

Q: Find the area between the curves y = e 1. = y = 2.3x + 1 from x = 0 to x = Area -0.4x and

A:

Q: Find the area between the curves: y=x^3-11x^2+18x and y = -x^3+11x^2-18x

A: y=x3-11x2+18x and y=-x3+11x2-18xTo find the area between the curves:

Q: Find the area between the curve x = y2 and the line x = y + 2 Solution : * with respect to x:

A: Given curves x=y2. . . . 1x=y+2. . . . .2 Equating (1) and (2) y2=y+2y2-y-2=0y-2y+1=0y=2,-1

Q: - Determine the area bounded by the curves y = -1² – 16x + 80 and y = (x – 4)°.

A:

Q: Calculate the area between the curves x = 1– y² by the line x = y² – 1.

A:

Q: Find the area between x-axis and the curve defined by   y = 2·x2 − 6·x on the interval [0,4].

A: Given curve: y=2x2-6x We need to find the area between x-axis and the curve on the interval 0,4

Q: Find the area between the curves y = 4x° and y= 3x + 1.

A: Given the curves y=4x2 and curve y=3x+1. We need to find the area between two curves.

Q: Find the area between the curves x=y^2/2 and y=x-4

A: First we draw the curves using graphing calculator.

Q: Determine the area bounded by the curves y = -r - 18z + 40 and y = (x- 2)2.

A:

Q: 3. Find the area bounded by the curve y 4sin(2x), the x-axis, and the lines x = 0 and x =

A: We have to find the area bounded by the given curves. We will find the area by the help of…

Q: Determine the area bounded by the curves Y = -x² – 18x + 88 and y = (x – 4)².

A: To determine the area bounded by the curves

Q: 12. Find the area bounded by the curve y = 3x(x - 2)² and the x axis.

A:

Q: What is the area bounded by the curve y^2=x and the line x-4=0?

A:

Q: Find the area between (bounded) by the curves y = x2 + 10x and y = 2x + 9.

A:

Q: Find the area bounded by the curve y=10+4x+x^2 and x-axis from x=-3 to x=-1.

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.