Find the area of the region enclosed by y = 2x - x -1 and y = x +x +2. when writing the answer as a mixed number, the integer part of the ,and the numerator of the fraction part is

Q: Find the total area of the region between the x-axis and the graph of y = - x´ - 3x, - 4 <x54.

A: Given query is to find the attached area of the region.

Q: Find the area of the region belowy = x3x+5 and above y = 3 for 3 < x <6. Area =

A: Proceed as shown below

Q: Find the area of the shaded region. y = x² +1 y = x -1 4 Enter the exact answer as an improper…

A: A=∫abfx-gxdx   for   fx≥gx

Q: 7. Find the area of shaded region of the rectangle: 2x + 4 4х — 2 X +1

A: Area of rectangle =length ×breadth  Area of shaded region  = (area of bigger rectangle- area of…

Q: Find the area of the region enclosed by: y = x³ and Y = = x4

A: Given curves are  y=x3 and y=x4 Point of intersection of the curves are obtained as follows.…

Q: Find the shaded area enclosed by y = 8x² and y = x* – 8x² within –4<x<4. y- &r y-x* - 8r

A: Consider the region bounded by the curves y=8x2 and y=x4-8x2 within the interval -4≤x≤4. Observe…

Q: Find the total area of the shaded regions. y=2-x -2

A: Provided figure is: The total area is divided into 3 regions A1, A2 and A3.

Q: what is the area of the region to the right of z=-0.98?

A:

Q: Use the rectangles to approximate the area of the region. (Round your answer to three decinmal…

A:

Q: Find the area of the region below y = x² + 2x 4 and above y = 3 for 2 < x < 5. %3D Area

A: Recall:            Area=  ∫abf(x)-g(x)dx  We have, f(x)=x2+2x-4, g(x)=3, a=2, b=5

Q: Find the total areas of the shaded regions: *+3y =2 x+y =0

A: First, find points of intersection of these two parabolas.

Q: Find the area of the region enclosed by y = 4- ², y = -x+2, r = -2, and r = 3.

A: Area under the curve is obtained by using the double integration  The integration is given as…

Q: Find the area of the 4+x enclased by y= +V x and y= 4

A: The area under the curve between two points an be found by taking the definite integral of the curve…

Q: Find the area of the shaded region. 9) y = /x y = x - 2

A: That's easy Have a great day!!!

Q: Find the area of the region below y = x² – 2x + 5 and above y 3 for 2 < a < 5.

A: To find area under the curve Shown below in shaded part

Q: Find the area of the region enclosed by the graphs of y = x² – 57, y = 519 – x³, and x = 0. (Use…

A: We have to find the area between the given curves.   As per our guidelines we can solve only one…

Q: Find the area of the shaded region. ¡y = x² +4 y y = x 4 -1 3 Enter the exact answer as an improper…

A: The objective is to find the area of the shaded region.

Q: Find the total area of the shaded region. 1.5- 1- (9,1) x- 9y? 0.5- 4.5 13.5 6.

A: To find the area of the shaded region

Q: Find the area of the region below y = x² + x – 4 and above y = 6 for 3 < x < 6.

A: • First, we need to sketch the given parabola and identify the region whose area is to be found.…

Q: Determine the area OF the region inside r= 4co520 but outside of +=2.

A: Two given curves are r=4cos2θ and r=2

Q: Find the area of the shaded region. y=x-4 y= /2x 2. 8. 10 x -4 2.

A: Given query is to find the area of tha shaded region.

Q: Find the area of the region between y = x2 + 9 and y = 2x + 10

A:

Q: Determine the area of the region enclosed by y3x^2 and y=x^1/2

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

Q: y = 3Vx, y= 20 – 2x.

A:

Q: Find the area of the region below y= x^2- 4x+11 and above y=6 for 3≤X≤5

A:

Q: Find the total area of the region between the x-axis and the graph. y = 2x° – 6x + 4x, 0sxs2 3 2

A:

Q: Find the area of the region enclosed by the graphs of y = 8 – 3x, y = 6 – x, and y = –5. (Use…

A:

Q: Find the exact area inside r=2sin2θ and outside r=√3.

A:

Q: Find the total area of the shaded regions. Ay 40 y = 4x (3,36) 32 +3,36) 24 16 y=x*- 5x² -6 -4

A:

Q: Find the area of the region enclosed by f(x) = a – 2x² and g(x) = a = 2².

A: Please see the answer in Step 2

Q: Find the area of the region below y = x2 – 4x + 12 and above y = 4 for 2 < x < 5. Area =

A:

Q: Find the area of the region enclosed by y = 4 – x², y = –x + 2, x = -2, and x = 3.

A: Given: - The region enclosed by y=4-x2, y=-x+2, x=-2 and x=3 To find: - The area of the given region…

Q: Find the area of the region enclosed by x = y² and y = x−2.

A:

Q: Find the area of the region enclosed by y2 – 4x = 4 and 4x – y = 16 %3D

A: We need to find the area of the region bounded by y2-4x=4  and  4x-y=16. So first we need to sketch…

Q: Find the area of the region enclosed by = x2, y = 2x, x = 2, x = -2 %3D Give your answer to the…

A: The area is given by:A=∫-222x-x2 dx

Q: Find the area of the shaded region. y=2 y= 2sin(70x) -2. O 4+4 4 + 8

A:

Q: Find the area of the region bounded by the given y = 4ax, y = 4ax°, a > 0

A: The given curves are  y = 4ax y = 4ax3 Intersection point of both curves 4ax = 4ax3 4ax(x2 - 1) = 0…

Q: Find the area of the shaded region. Enter your answer as a reduced fraction. (-2, 3) (-2,-1)…

A: Given:              sx=3-x2tx=-x+1 point of intersection of two curves let:         y=3-x2…

Q: Find the Area of the region inclosed by x=y3 and x=y1/2-6

A: Please find the solution below:

Q: Find the area of the region enclosed by y = –x² +6, y = x, y = 5x, and x > 0.

A:

Q: Find the total area of the shaded region. 1.5- 1- (9,1) x= 9y? 0.5- 0. 4.5 13.5 6.

A:

Q: Cross section area given by A(x) - (4 - x) 2, osxs4 128 128 O o o

A: Given,           Cross section area is given by Ax=π1284-x2, 0≤x≤4.To find: The volume of the…

Q: Find the area of the shaded region. f(x) = x – 8x° + 21x, g(x) = 20x + 50 3

A: Intersection…

Q: Find the total area of the shaded regions. 10 (-2,8 8- (2,8) jy%3D2X' ty=2x2 6- 2- y3x 2x -4 -2 2.…

A: Here we need to find the area bounded by the curves y=2x2 and y=x4-2x2.

Q: Give the area of the region enclosed by y=2- x and y=x²

A: To find the intersection of both graphs, set the equations equal to each other and solve for x

Q: Find the area of the region enclosed by y = x² – 2x and y =3.

A: Our objective is to find the area.

Q: Find the total area of the shaded region below. 1 x+ y = 2 y = x2 1 2

A:

Q: 8. y = 3x² – 3, -2< xs 2

A:

Q: Find the area of the region that is enclosed between y = 14x? – x³ + x and y = x2 + 41x. The area is

A: We need to find area enclosed under the curve.

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.