X = y 12 x = 216 / y? 12

Q: 1. Find the area of the shaded region. 3 y = Vx X 4 y = -x а.

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: Shade the area of the region bounded by, x² + y? p Hence, find the area of the specified region…

A: we use integration to find area between curves

Q: Find the area bounded by the lines and curves y = x? - 2 and y = 2

A: Graph:

Q: Find the area between y = 2x and y = x° from x = 0 to x =7

A: Given: To find the area between the curve y=2x2 and y=x3 from x=0 to x=13   Definition: If f(x)≥g(x)…

Q: What is the area of the region enclosed by the curve y=e^x and the lines x=-1 and y=3?

A:

Q: : Find the area of the region in the first quadrant that is bounded above by y x and below by the…

A: SOLUTION-

Q: 3. Find the area of the region between y = x2 and y = 2x; approximate the area of the region using…

A: We have to solve given equations for x limits

Q: Find the area of the shaded region. y 2+ y = x+ – 2x3 1 y = 0 2 -1 i

A: Given, The function  ; y = 0   and  y = x4 - 2x3  the limits : x = 0  and x = 2 We have to find the…

Q: Find the area of the region between the curves y = 12 – a? and y = x² – 6. Area between curves =

A:

Q: Find the area of the region in the first quadrant that is bounded above by y = √x and below by the…

A: Now the diagrammatic representation of the area is,

Q: Find the area bounded by the curve y = 8 – x and both coordinate axes in the first quadrant. Area of…

A:

Q: Estimate the area under the curve y=64-x^3 between x=0 and x=4. Use four rectangles

A:

Q: Find the area of the region between y² = x and x = y +2.

A: Given,  y2 = x   and  x = y+2  We have to find the area of region between y2 = x   and  x = y+2

Q: 2. I3D X-に-A

A: To find: Area of the shaded region in adjoining figure.

Q: Find the area between y=x2-x2 and y=x2. Sketch the region

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

Q: Find the area of the region between x = 2y and x = y3 — y.

A: Given x=2y and x =y3-yThe area between f(x) and g(x) are two continuous functions and  f(x)≥g(x)  on…

Q: Find the area between y=x4-x2 and y=x2 . Sketch the region

A: given  y=x4-x2 and y=x2 intersection  x4-x2=x2x4-2x2=0x2(x2-2)=0x2=0   or x2-2=0x=0    or x2=2x=0…

Q: Find the area of the region between the curves 4x + y? = 12 and z = y. Area between curves =

A:

Q: Find the area between y= x4-x2  and y=  x2 Sketch the region

A: Solve by integration

Q: Find the area of the shaded region below. у y =Vx 2 x=2 1 y=- x1 Area

A:

Q: y (0, 3) y = 1 - sin (x - T/2)

A:

Q: Find the area between y = x* - x² and y = x². Sketch the region.

A: You have posted multiple questions. As per the instruction, we will be answering only the first…

Q: Find the area of the region bounded by the curve y = 9 - x2 and the x-axis. Answer:

A:

Q: Find the area between the curves. 1/5 6/5 y=x y = 4x¹ The area between the curves is (Do not round…

A:

Q: Find the area of the region between the curves y = 12 - x² and y = x? – 6. - Area between curves =

A: Given curve :

Q: Find the area bounded by y = 2x2 - 4 and y = 5. Leave your answer correct to 2 decimal places.…

A: This is area under the curve problem

Q: Find the area between x = 1- y² and y = -x - 1. Sketch the region.

A: We will use double integration to find area bounded

Q: Find the area bounded by y=2*, y = 2x2, the y - axis and x = 1 Write your final answer in two…

A:

Q: Find the area of the region between the curves y = x| and y = x? – 2. Area between curves =

A:

Q: Find the area of the region between the curves y = 12 – x and y = x* – 6. Area between curves =

A:

Q: Find the area of the region bounded by y = x³ - 8 the x-axis and the y axis.

A:

Q: Find area of the region under the curve y=x^3−9 and above the x-axis, for 5≤x≤7. area=

A:

Q: problem in photo attached

A: Given:

Q: Find the area of the shaded region. y =x – 2 2- y= Vx 1+ + 3 4 -1 square units 2.

A: Given that: To find: Area of the shaded region.

Q: Find the area bounded by y=2%, y = 2x2, the y - axis and x = 1 Write your final answer in two…

A:

Q: Find the area bounded by y = 2 - x squared and y = x

A:

Q: Find the area of the shaded region (using the area between two curves). y=x2 - 4 y=2x² •x - 6

A:

Q: Shade the area of the region bounded by, x? + y? s p? and |x| + \y] > p Hence, find the area of the…

A: Answer

Q: Find the area bounded by the indicated curves. y 2x, y 4-2x, x = 0 (x20) The area is

A: Given; y=2x^2, y=4-2x , x>0

Q: Find the area of the shaded region. y 3 y = Vx (1, 1) x = 8 2 8. 2)

A: We have to find the area of the shaded region.

Q: Find the area of the region between y2=x and x=y+2

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

Q: Solve the area bounded by y^3+10=x^2, the lines y=-2 and y=2

A: Given: The curve is y3+10=x2 and lines are y=-2 and y=2 To find: Area

Q: 8 y = 2x and æ = Determine the area of the region bounded by y 4.

A: We need to determine the area of the region enclosed between y=8x , y=2x , x=4 Now, in the graph…

Q: Find the area of the region enclosed by y = x? and y = Vr.

A: We first sketch the region using a graphing calculator  y=x2 (green) y=sqrt(x) (violet)

Q: Find the area bounded by the given curves. y = 3x2 and y = 27

A: The given curves are y = 3x2 and y = 27.

Q: Solve by integration: What is the area of the region enclosed by the curve y=x(x-1)(x-2) and the…

A: See the attachment

Q: Find the area bounded by the curve y = 4x - x² and y = 3. Answer:

A:

Q: Q1: Find the area of the region bounded by y= Vx, y v4-x and x-axis.

A:

Q: Find the area of the shaded region. У 3 x = y - 2 y = 1 x = ey -3 -1 y = -1 -3 3. 2. 2. 2.

A: To find the area of the shaded region which is bounded by the below functions.

Q: Find the area of the shaded region.

A: To find: The area of shaded region. Concept used: Area (A) under the curve y=fx in the interval a to…

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.