Sketch the region whose area is given by the definite integral. 36 - x2 dx y y 12 35 30 25 20 15 10 2 -6 -4 -2 2. 4 -4 -2 2. y 5 5 4 4 3 3 2 2 1 -4 -2 2 6. -4 -2 2 4 6 10

Q: Find the area bounded by the curve 2x² + 4x + y - 0 and the line y+x=0 a. 1.000 b. 1.125 c. 1.525 d.…

A: We will first sketch the curve and the line.

Q: Set-up the integral to calculate the area of a region bounded by x-y=3 and y=x2 -6x+9 ? A dy dx x2-…

A: Graph:

Q: Sketch the region R whose area is given by the iterated integral. *16 – y² dx dy 14 12 10- y 8. 4 2-…

A: Solve by using graph

Q: Determine the area bounded by the curve y = 2x – x² + 5 and the line joining the points (3,2) and…

A: Given, The curve  y = 2x-x2+5  and the line joining the point 3, 2  and -2, -3   We have to find the…

Q: Find the area of the region bounded by the graphs of the given equations. Ay 31- y = 9x, y = x³, x =…

A: Given,  The equation of the curve  y = 9x   and  y = x3 We have to find the area of region bounded…

Q: 3. Find the area of the region in the first quadrant that is bounded above by y = vx and below the…

A: Solution

Q: Sketch the region whose area is given by the definite integral. 50 40 30 20 10 6 6 50 40 30 y 20 10…

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Q: D. Use double integration to find the area of the region R enclosed by the parabola y = 4-x² and the…

A: Let's find area by using double integration.

Q: Find the area bounded by the curve 2x² + 4x + y − 0 and the line y + x = 0 a. 1.000 b. 1.125 c.…

A:

Q: Sketch the region whose area is represented by the definite integral. dx y 12 12 10- 10 8. 6 6 10 2…

A: The definite integral can be used to evaluate area of region bounded by curves. If over an interval…

Q: | Consider the area between the graphs x + 2y = 20 and x + 4 = y² . This area can be computed in two…

A: Consider the area between the graphs x+2y =20 and x+4 =y2 First of all it can be computed as a sum…

Q: Consider the following. y = x2 y = 12 - x 16 14 12 10 6- 2 4 6 8 10 12 (a) Find the area of the…

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Q: Consider the following. y = x2 y = 12 - x 16 14 12 101 8- 6- 8 10 12 (a) Find the area of the region…

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Q: What is the area of the region bounded above by y= sin x below by y=x- T and from the left by the…

A:

Q: (a) Evaluate the Integrals:  ∫{2x^2 + 3}/{x(x − 1)^2}dx b) Find a horizontal line y = k that…

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Q: Write a definite integral that represents the area of the region.                        g( y) = y3

A: Given  g(y)=y3

Q: Consider the following. y = x2 y 20 - x 25 20 15- 10- 5- -10 -5 10 15 20 (a) Find the area of the…

A: Topic = Application of integration

Q: Set up the definite integral required to find the area of the region between the graph of y = 12 -…

A:

Q: Which one of the integrals gives the area of the region bounded by y = x- -4x and y = 0? a) None is…

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Q: 9. Approximate the value of the integral defined by the given set of points. dx कडोे इंत्र संडझ वौै…

A:

Q: Consider the following. y = x2 y = 12 - x 16 14 12 10 y 8. 6. 2 4 6 8 10 12 (a) Find the area of the…

A: Recall: Area , A=∫x=ax=bf(x)-g(x) dx ; where f(x)≥g(x) Area,A =∫y=cy=df(y)-g(y) dy ; where…

Q: |-4 Find the area of the shaded region. 3. yA 4. yA x= y? – 4y x= y? - 2 y=1 (-3, 3) x=e y=-1 x= 2y…

A: A= ∫y=-11…

Q: se a double integral to find the area of the specified region. y y = 1 8 21

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Q: Sketch the region whose area is given by the definite integral. xdx y 10 10 10 35 8 30 25 6 6 20 4…

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Q: Express the area of the region bounded by the given lines as an iterated double integral. The…

A:

Q: Given the functions: 1. y = 0.1sin((x+0.15)/-0.1) +0.1 2. 6y=x^2-10 Find the area of the region…

A: Let R be the region bounded by the curves y=0.1sinx+0.15-0.1+0.1and 6y=x2-10 the region is shown in…

Q: y. x= y? – 2 y = 1 x= e" y =-1

A: Given the graph of a region

Q: Set up the definite integral that gives the area of the region. Yı = (x – 7)3 Y2 = x – 7 dx J6 y 1.5…

A: Given problem:- Set up the definite integral that gives the area of the region. Y1 = (x-7)³ Y2 = x -…

Q: Find the area of the shaded region. A. In 2 В. Зln2 C. 2 In 2 3- 2.5- D. 2 In 3 2- 1.5- y= X 3D 1-…

A: To find the area

Q: Find the area bounded by the given curves. y = 2x - x2, y = 2x- 4 32 O A. w/ 3 37 OB. 3 31 OC. 3

A: The objective is to find the area bounded by the given curves

Q: Draw the region whose area is given by the definite integral. Ay 40- Sa2-2 36 - 2x)dx 32- Use the…

A:

Q: Set up the definite integral that gives the area of the region. Yı = 7(x³ – x) Y2 = 0 dx y 3 2 -1.5…

A:

Q: The area of the region is given by the definite integral [f(x) – g(x)]dx y = 2x – 3 y = x² – x – 7

A: One of the two main parts of calculus is concerned with the study of integrals, as opposed to…

Q: Find the area of the shaded region. 22) y = (x 3)2 (2,1) (4,1) 4. C)- D) Evaluate the integral. 31/4…

A: Other

Q: Consider the following. y = x2 y = 6- x 10 8 6 4 2- -2 4 (a) Find the area of the region by…

A:

Q: 1. Find the area of the shaded region by (a) integrating with respect to x and (b) integrating with…

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Q: 3/ Find the area of the region enclosed between the curves y= x' and x= y مساعدة 1.8 هذا رسم ل…

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Q: Consider the region on the 1st quadrant bounded by y = √√4x²,x and y - axes. If the region is…

A: Using shell method, given format is obtained. From this format, evaluate m-n.

Q: A region is bounded by the y=x² and y=6x-x² Which of the following integrals would approximate the…

A: We can solve this as follows:

Q: Set up the definite integral that gives the area of the region. Y1 = x2 – 5x Y2 = 0 dx 3 * 4 6 12,…

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

Q: Determine the area of the region between the two curves in the given figure by integrating over the…

A: We will find the area between the two curves as following

Q: Q 3:- Set up an integral that can be used to determine the area of the bounded region by the gra of…

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Q: A region is bounded by the y=x² and y=6x-x2, Which of the following integrals would approximate the…

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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?…

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Q: Set up the definite integral that gives the area of the region. Y1 = x2 + 2x + 4 Y2 = 2x + 8 dx -2

A:

Q: 4 / Find the area of the region enclosed between the curves y%3= cos 2x, y=0, x-TT/4, x- TT/2 ? ans/…

A: we allowed providing one solution at a time. Please upload the rest questions seprately.   Question…

Q: 1) The region R in the first quadrant is bounded from above by y = 2x+9 and below by y = x² +3. Find…

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Q: Set up the definite integral that gives the area of the shaded region bounded by the graphs of y,…

A:

Q: Set up the definite integral that gives the area of the region. Y1 = x2 + 2x + 5 Y2 = 2x + 30 %3D…

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.