me center and radius of the circle (x – 1)² + (y + 5)² = 3. e center and radius of the circle x² + y² + 4x – 4y + 4 = 0. %3D

Q: Find the area of the shaded region. y = JX - 3 (16,1) 16 (0,-3) Select one: A. 22 В. 38 3 O C. 16 D.…

A: Area of shaded region can be find as follows

Q: Q.2) The basts of the equatioon y'' + y" = 0,are: b) 1,1.e a) 1,1.e c) 1, x,e²* d) 1,x.e" 0 about

A:

Q: Find the area in square units bounded by the following; (Show graph and detailed solution. Locate…

A: The given function is y=x3+1. Sketch the region bounded by y=x3+1, x-axis from x=0 and x=3 as shown…

Q: 2x2+4x+4 Estimate the area of the curve y = 2 from x = 1 to x = 3 by using 5 rectangles and right…

A: We find out the area of given curve usin Rieman sum where dalX=(b-a)/n where n is the number of…

Q: S-Region inside the circle (r=6on the right of the line (x=3).

A: Given that - Region inside the circle (r=6) on the right of the line (X=3)

Q: x2 + z2 = 7 Write an equation for the cross section at  y = −7 using x and z. Write an equation…

A:

Q: Q3:B/ Find the areas of the regions enclosed by the line and the curve y = x* – 4x? + 4 and y = x?

A:

Q: the Pollowing Cx-)CX-2) di So lVe DE 2. + y =X %3D

A: The given linear differential equation is Dividing both sides by (x-1)(x-2) The given differential…

Q: y 4 A y = 4* 3 2 y = 2* 0.5 1

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

Q: y =z² y = r³ - 12r Which of the following gives the shaded area? ........

A: If we have two curves y= f(x) and y=g(x)  such that f(x)>g(x) then the area between them bounded…

Q: Q 04: Consider a rectangular garden whose area is (5R + 230) square meters. On one side of the…

A:

Q: What region in R° do each of the following equations represent? Explain your reason- ing. (a) x2 +…

A: Consider the provided question, (a) Given, x2 + y2 = 49 We have, x2 + y2 = 49 or x2 + y2 = (7)2…

Q: Find the area enclosed by the x-axis and the curve y=4-x2. A 18 square units 32 B square units 3 ©…

A: topic - area under the curve

Q: 1. Find the area bounded by the parabolas y? = 4 and y²+12x = 36 2. Find the Area bounded by the…

A: Given :     Curves and find area by integration

Q: Find the area of the shaded region. y x = y - 7 y = 1 x = ey -4 -8 -2 2 4 -6 y = -1 -2 -3 2.

A: We have to find the area with respect to y here. To find the area between x=e^y and x=y^2-7 we have…

Q: Find the area of the region enclosed by the curves y2 - 4x = 4 and x -y= 2. The area of the region…

A:

Q: Find the area of the loop of the curve y^2=x^4(x+4) complete solution

A: The solution is given below

Q: S(x) = If the crate has the least possible surface area, find its dimensions. meters y = meters…

A:

Q: Find the area A of the region between the graphs of the equations y? = 9x x2 = 9y A = 27 9.

A:

Q: Q2: Find the area of the region inside the circle r = 2cos0 and outside the circle r = V3. Graph the…

A:

Q: ind the area of the shaded region. y 2 x = y - 6 y = 1 x= e -4 -2 2 4 H y = -1 -2 -31

A:

Q: Find the area of the shaded region. y x = y -8 -6 -4 -2 4 Hy=-1 2.

A:

Q: Y Classify the y'ty lax =0 differantial equation and find Hs general ookution.

A: First order separable ordinary differential equation

Q: Find the area of the surface. The portion of the paraboloid z = 64 – x - y²in the first octant

A:

Q: ented square v V , (0, 1). The va + 8x² y dy)

A:

Q: N. (2 Y - x ) dA,where R is the region of the first quadrant bounded by the circle x2 + y? = 4 and…

A:

Q: Find the area of the shaded region below. y = 3x - 3 y=-x + 3x +6 WCOLLEGE KL

A: We have to find the area under the curves.

Q: y=x² +2x+1 and y = 3x +3 The area of the plane region is?

A: "Since you have asked multiple questions, according to our guidelines we will solve only the first…

Q: Find the area of the region enclosed by the curves y2 - 4x=4 and x -y= 2. The area of the region…

A: To find the area enclosed by the below curves. y2−4x=4 x-y=2

Q: 23. The diagram shows the curve y = x2 – 6x – 2 and the line y32x-9, which intersect when x=1 and…

A:

Q: Find the area of the region enclosed by the curves x + y² = 0 and x + 4y² = 12. The area of the…

A:

Q: a) Find the area of the curve x²/3 +y2/3 = a²/3 %3D

A:

Q: Q3: Find the points on the surfac x^2+z^2-4=D0, closest to the origin.

A: Solution:-

Q: The student should answer the question below: Evaluate the given equation: | ydA where T is the…

A:

Q: y = e* - Tese x. What is y'= TescX %3D y!? 2. నా

A: Given, y=ex-πcscx We have to find y'.

Q: Find the total area of the shaded region. Ay 12 10- 8- 6- 4- y=x NO 2- Co y=7 y= 2 X 28 8 10 12 14 >…

A:

Q: Q3) for what values of (m) do the line ( y mx ) and the curve (y enclosed a region ? find the area…

A: There will be enclosed area only when both graphs cut each other at multiple points.  If graphs cuts…

Q: Inside the sphere x2 + y2 + z2 = 16 and outside the cylinder x² + y? = 9 %3D

A: The mathematical expression to calculate the volume by double integral. V=∫∫f(x,y)dA=∫∫f(x,y)rdrdθ…

Q: (4x - y) dA, where R is the region in the first quadrant enclosed by the circle x2 + y2 = 16 and the…

A: Solution :- To find ∫R∫(4x-y)dAWhere R is the region in the first quadrant enclosed by the circle…

Q: The graph of y = g(x) is shown below. The areas trapped between the curve and the x-axis are given.…

A: Definition used -                           ∫abf(x)dx=∫abf(u)du…

Q: 5. Find WX in the trapezoid. P 27 Q X 39 S W R

A:

Q: Find the area of the region between the line y = x — 4 and the parabola y2 = 2x

A:

Q: Find the area of the shaded region. r = 4 + 3sin(0) 6- y -6 -2 6. 2.

A: Given that: r=4+3sin(θ)

Q: 4.8 12 4.8° X. at Response

A:

Q: Find the area of the shaded region. y x = y - 4 y 15 5 4'2 2 -6 -5 -4 3 -2 X= y-y -2 -4 -6F

A: Given, The right function   x = y -y2  and left function     x = y2 - 4y Point of intersection of…

Q: a of the shaded region. y 3- = y² -7 x y= 1 X= -8 -6 -4 4 Hy = -1 -2 2. 2. 2.

A: area under the curve can be calculated as:-

Q: Find the area of the region enclosed by the curves x+ y =0 and x+6y = 20. The area of the region…

A:

Q: The area of the shaded region: y-24 -1 (1.2) 2 3 5n

A:

Q: Find the area of the shaded region. y = e" 4 -1 1 (e - 1)/4 4e 1/4 e/4

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.