a) Sketch and find the area of the region determined by the intersections of the curves. y = x² – 1, y =7– x²

Q: sketch the region enclosed by the carves and find its area X Sy + 1a = .....

A: The detailed solution is explained in steps 2 and 3.  First we have to sketch the curves and then…

Q: Find the area of the region enclosed by one loop of the curve  r= 3cos 40

A: We have to find the area by one loop of the curve r=3cos4θ We know area A=12∫-aar2dθ for cosθ we…

Q: 15. Sketch the region enclosed by the lines x = 3 and y = 1 and the curve xy = 9, and find its area.

A: The area between curves is the area between a curve fx and a curve gx on an interval a, b given…

Q: In this item, sketch the region enclosed by the given curves. Then find the area of its region. 1.…

A: We need to find area.

Q: Sketch the region and find its area (if the area isfinite).   S = {(x, y)  x ≥ 1 ,  0≤ y ≤ 1/(x3+x…

A: Consider the equations in the given statements. First of all we will plot the curves and find out…

Q: 16. Sketch the region enclosed by y = |x| and y = x2 - 2, and find its area.

A: To evaluate the area between the following curves

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

A:

Q: a) Sketch the region enclosed by the curves y = 12 – x², y = x² – 20. - - b) Find the area of the…

A:

Q: Consider the infinite region in the first quadrant bounded by thegraphs of y = 1/x2 , y = 0, and x =…

A:

Q: 4. Find the area of the region bounded by the horizontal strip. y² +1 and the y-axis using

A: Topic = Area

Q: Consider a triangle of area 2 bounded by the graphs of y = x, y = 0, and x = 2.   Sketch the region?

A: First draw the x and y axes . Label x for x-axis and y for y-axis . Line y=0 passes from the point…

Q: Sketch the region and find its area (if the area isfinite). S = { ( x, y) | x > = 0 , 0…

A:

Q: Evaluate , (2x + y²)dA over the region R in the first quadrant bounded by the axes and y? = 1-x. -1…

A:

Q: 3. Find the area of the region bounded by the parabola y? = 2x – x and the line y = x – 5 by taking…

A: We have equation of parabola  y2=2x-xy2=x                                                     ……(1)…

Q: Sketch the region bounded by the given curves, then find its area. 2. x = y2, x = y +6

A:

Q: 1. Find the area of the region bounded enclosed by the parabola y? = x and x? = y. %3D

A:

Q: 1. Sketch the region enclosed by the given curves and find its area. y = x?, y = x*

A:

Q: Given the region bounded by the graphs below, find the area of the plane region. y=3x+3 and…

A: First recognise the region bounded and  find where they intersect each other. Accordingly find the…

Q: 3. Sketch the region enclosed by the curves y=-x +3x and y = x. Hence, find the area of the region.

A: We have to find the area

Q: Sketch the region and find its area (if the area isfinite). S = { ( x, y) |   -2< x <= 0  , 0…

A: The sketch will be as follows

Q: find the area A of the region R enclosed by the line y=1/2x and the parabola y^2=8-x. sketch graph…

A:

Q: 3. Sketch the region enclosed by the curves/lines x = y, y =÷, x = 3 and find its area.

A: Given equations: x=y……1y=1x……2x=3……3

Q: Sketch the region and find its area (if the area isfinite). S = { ( x, y) | x > = 1 , 0…

A:

Q: Consider the infinite region in the first quadrant bounded by thegraphs of y = 1/√x, y = 0, x = 0,…

A:

Q: Sketch the region enclosed by the given curves. x = 6y?, x = 1 + 5y?

A: To sketch the region enclosed the given curves:- x = 6y2x = 1+5y2

Q: ind the area bounded by the given curves. 1.) 2x+1, x+y=7, x=8 2.) y^3=x^2, x-y=2, x+y=2

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

Q: Given the curve y = x´ and the lines y = 0 and y = 2 – x Find the area of the region bounded by the…

A: Given

Q: Find the area of the region enclosed by the graphs of 1 VI- 472' Y =0, x = 0, and x = 4' 1 — 4г?

A:

Q: Sketch and find the area of the region lies inside the cardioid (r = 1+ cose) and outside the circle…

A:

Q: Find the area enclosed by the given curves. y = csc 2 x, y = cot 2 x, » 7, and x = 00

A:

Q: 15. у з ,y = 1+x? Y = |x|

A: Accoding to Given Question no 15 only

Q: Sketch the following region enclosed by the following curves and find its area. y = x, y = a, x = b,…

A:

Q: 1) Sketch the region bounded by y = 1– x and y = x2 – x and find the area of this region. 2) Sketch…

A:

Q: Sketch and shade the region bounded by the graphs of X = y? +1 and x + 2y = 4 and find the area of…

A:

Q: Sketch the region enclosed by the curves y = 2 sin(x), y = 2 csc²(x), x = 7 and x = 4, and compute…

A: The given curves are: y=2 sin x,       y=2csc2x,       x=π4      and      x=3π4

Q: 5. Sketch the region enclosed by the given curves and find the area bounded by the curves y = Vx –…

A:

Q: 1. Sketch the region enclosed by the given curves and find its area. y = x², y = x*

A: Answer

Q: Find the area of the region enclosed by the given curves y=cosx y=1-(2x/pi)

A:

Q: 2. Find the area of the region enclosed by æ + y? = 0 and ¤+3y² = 2.

A:

Q: Find the area of the region enclosed by the given curves. 1. y = e*, y = x² – 1, x = 0, x = 2.

A:

Q: Find the area of the region enclosed by the curves x + y² = 3 and 4x+ y? 0 %3D

A:

Q: Find the area enclosed by the given curves. y = 2x - x 2, y = 2x - 4 O 32 O 34

A: The given question can be solved as shown in step 2.

Q: Find the area of the region described in the following The region bounded by y = 2 - IxI and y = x?

A: y=2-x and y=x2 The graph is,

Q: 2. Determine the area of the region bounded by x = y? – 4 and y = and sketch a graph of the region.

A: We graph the region using a graphing calculator  y=x/3 (red) x=y2-4 (black)

Q: Determine the area of the region between the x-axis and the graph of the curv -1 from x- 0 to x- 4.…

A: Area bounded by curves :   If f(x) and g(x) are two continuous function on a,b and f(x)≥g(x) on a,b…

Q: 19. y = x - 4x+ 3x, y = 0

A: Sketch the graph of the curve, find the point of intersection of the curve with x-axis and calculate…

Q: 4- Find Ix and Iy For The Region Bonded by y=x² and y=Vx 5- Find the area of The Cirde x+9=4 From…

A:

Q: etch the region enclosed by y = x²y = √√x,x = 0,x = 1 and find its area.

A:

Q: 1. Sketch the region R between the graphs of y = |r], y = x² – 1. Find the area of the region R.

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.