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

Q: (13) Find the area of the region between the line y = 2x and the curve y =x² +x-2 %3D

A: The given two curves are y = 2x y = x2 + x - 2

Q: Find the area of the region bounded by the three curves y = x^2 , y = 8−x^2 , and 4x−y + 12 = 0.

A:

Q: 1/ Find the area of the region enclosed between the curves y= 2r'+10 and y=4x+16 and ,x=-2 and x=5?…

A: The area of the region enclosed by the given curves has been obtained below.

Q: 1. Find the area of the region enclosed by the parabola y = 2 – x² and the line y = -x.

A:

Q: Determine the area of the region bounded by the curve y = x³ – x² – 2x, and а. the x-axis b. the…

A: Note: As you asked only part (b) so, I answered here only part (b).

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: 2. Find the area of the region enclosed by the parabola y = 2x² and the line y = -x-1

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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 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: Determine the area of the region between the following curve. x = |y| and 2x = −y^2 + 2

A: Given that, x = |y| and 2x = −y2 + 2

Q: Find the area of regions enclosed by curves y x3 – x + 3 and y = x2 + 5x + 3.

A: Given equations of the curve are:                              y=x3-x+3& y = x2+5x+3

Q: 3 Find the area of the region bounded by 2x = y² +1 and the y-axis using the horizontal strip.

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: Find the area between the curve  y = x2 + 3  and the line  y = 2x − 2  (shown below) from x = 0 to…

A: We first sketch the area using a graphing calculator

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

A: According to our guidelines we can answer only first question and rest can be reposted.

Q: 2. Determine the area of the region bounded by the curve y = x³ – x2 – 2x, and а. the x-axis b. the…

A:

Q: Find the area of the region between the curves y = x x-1 and y =-2x+2 from x = - 1 to x= 1.

A:

Q: Find the area of the region under the given curve from 1 to 6. x2 + 6 y = 7x — х2

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

A:

Q: Compute the area of the region enclosed by the x-axis and the curve y = x3 - 7x2 + 10x

A:

Q: Find the area of the region bounded by the parabola y^2=x+3 and the line x - y = -1

A: Given: Parabola: y2=x+3 and line : x-y=-1 To find : Area of the region bounded by the given parabola…

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

A:

Q: Find the area of the region bounded by the given curves.  y=x^2-4x, y=3x+8

A: Let the curves be: The area between curves f(x) and g(x) on an interval [a,b] is given by: Where,…

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: 2. Find the area of the region enclosed by the parabola y = 2 - x² and the line y = -X.

A:

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

A: The given region is bounded by 2x=3y2+1 and the y-axis.

Q: A\ Calculate the area of the segment cut from the curve y =2x2 by the line y = x+1 with x2 0.

A:

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

A:

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

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 region bounded by the curves x= 2y+6 and x y-1.

A:

Q: Find the area between the curve y = sec (4x) and the line joining the points (-,2) and (. 2).

A: Consider the given information: To find the area between the curve and the line joining the points.

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

A:

Q: 1- Find the area of the region enclosed by the line y=4x and the curve y=x³ + 3x.

A: To. Find thhe area of enclosed region

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 between the curves y=x2-1 and y= - 2x² +2 from x= - 1 to x=1.

A:

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: (b) Find the areas of the regions enclosed by the line y = x and curve y = x- 3x

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

A:

Q: Find the area of the region bounded by the graph of y = 2x2 − 3x + 2 the x-axis, and the vertical…

A:

Q: 7) Find the area of the region enclusced by the curves y=x² and

A: Please refer the attached image for complete solution. THANK YOU !

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

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: 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 enclosed by the curve y=x2-2 and by the line y BO 2. y=x²-2 y=2 Co

A: The equation of the curve is:                                            y=x2-2  The equation of the…

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.