2. The region is bounded by the curve y = x(x + 4), the x-axis and the line x = 3. Find the following: a. Area b. Volume generated if the area is revolved about b.1.х - ахis b.2. x = 3 b.3. у-аxis c. Locate center of gravity

Q: The region in the first quadrant that is bounded above by the curve y= 1/x, on the left by the line…

A:

Q: Given an area D bounded by curve y = 4x−x^2, line x+y = 6, and y-axis. Find the volume if the area D…

A: We are given an area D bounded by curve y = 4x - x2, line x + y = 6, and y-axis. We need to find the…

Q: 1. If the region bounded by the two curves is revolved about x = 4, what is the volume of the…

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Q: 15 - Which of the following is the volume of the object that occurs when the region bound by the y =…

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Q: 2. The area of the parabola x2 = 4y – 4 cut through its latus rectum is revolved about the…

A: 2) Parabola; x2=4y-4End points of the latus rectum (-2,2) and (2,2)vertem = (σ 1)using washer method

Q: Sketch the region enclosed by the given curves. y = 17xl, y = x2 - 8 y 40 4아 20 20 ma x -20 -40 50…

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Q: 1/ Draw the functions , 2/ Find the volume of the solid generated by revolving region bounded by…

A: the given question is taken from calculus in which we have to find the volume of solid generated by…

Q: 6. What is the volume generated when the area in the first quadrant bounded by the curve x? = 8y,…

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Q: 3]. , Let V = ar²h, where V the volume of a right circular cone of radiusr and height h. Show that…

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Q: Given the area in the first quadrant bounded by the curve x^2 = 8y, the line x = 4 and the x – axis.…

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Q: What is the volume of the region bounded by the lines f (x) = x²,x = 2, and y 49 rotated about the…

A: Given data:     The given equation is: f(x)=x2. The second equation is: x=2. The third equation is:…

Q: 2. Find the volume oF solid obt ained by revolving the region bounded by the about the x- axis the…

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Q: 10. Find, among all right circular cylinders of fixed volume V, the one with smallest surface area…

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Q: 1. Calculate the volume bounded by y = x², y = 0 and x = 2 rotated about the specified line, using…

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Q: What is the volume (in πcu. units) of the region bounded by the curve y=x^3, and the lines x=1, x=2…

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Q: 1.) Find the area of the region bounded by the curve ya 12 and the lines y=o, y=x, x=2.

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Q: Sketch the region enclosed by the given curves. x = 9y?, x = 8 + 7y? y 35 21 30 25 20 5 10 15 20 25…

A: With the help of the graphing utility the area enclosed by the curve of the given equation is shown…

Q: 1) Find the volume formed by rotating the region enclosed by: x = 3y and y³ = x with y ≥ 0 about the…

A: answer is in next step . please give a like!!!

Q: Find the volume (in cubic units) of the region bounded by the curves (y – 1)° = x – 1 ,and the lines…

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Q: Given that R is the area bounded by the curve y = 9 – x^2 and y = 5. Calculate the volume of the…

A: Given that R is the area bounded by the curve y=9−x2 and y=5. We have to calculate the volume of the…

Q: Find the volume of the area bounded by the line y = 3x + 4 and the curve y = x² if it is revolved…

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Q: Find the volume (in cubic units) of the region bounded by the curves (y-1)' = x – 1 ,and the lines y…

A: We have to find the volume of the region bounded by curvesy-12=x-1 and lines y=-1 and y=2when…

Q: 12 - Which of the following is the volume of the object that occurs when the region bound by the…

A: We sketch the region using a graphing calculator  The shaded region is rotating about the y axis

Q: 14. Find the volume tended by the graph of f(x, y) = 1+2x + 3y, the rectangle [1, 2] x [0, 1], and…

A: Given function is: fx,y=1+2x+3y and the coordinate of the rectangle is: 1,2×0,1

Q: 2) Find the volume generated by the area bounded by y = x², y = 4x, revolved about x-axis.

A:

Q: The region in the first quadrant that is bounded above by the curve y = 1/(x^1/4) , on the left by…

A: Solution Given The region in the first quadrant that is bounded above by the curve y = 1/(x^1/4) , on…

Q: I Sketch the area bounded by x² + 2y = 4 and x+y+2=0 and determine: d) area using horizontal strip…

A: Solution is given below:

Q: and y=2 8) x = y² +1₁ x = 0, you, The most appropriate method to use to find the volume generated by…

A: The given region is x=y2+1,x=0,y=-1 and y=2. Find the volume generated by revolving the region about…

Q: The region in the first quadrant that is bounded above by the curvey = 1/x1/4, on the left by the…

A: Given: The region in the first quadrant that is bounded above by the curvey=1x14 on the left by the…

Q: 1. Find the volume of a solid if the area boun ded by the curve y = In x, the x-axis and the line x…

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Q: Given a curve having an equation of y2 = 4x. a) Compute the area bounded by the curve and the line…

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Q: Find the volume of: the area bounded by the curve y2 = 9x and the line x = 4 revolved about x = 4.

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Q: Find the dimensions of a right cone with surface area S=4 n that has the largest volume?

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

Q: I Sketch the area bounded by x² + 2y = 4 and x+y+2=0 and determine: d) area using horizontal strip…

A:

Q: Given the area in the first quadrant bound by x² = 8y, the line x = 3 and the x-axis. What is the…

A: Use the formula for volume obtained on revolving a dingle function. Determine the limits and the…

Q: Find the area enclosed by the closed curve obtained by joining the ends of the spiral r= 98,0 < 8<…

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Q: Find the volume generated by the region bounded by the curve y 12X and the line X3 rotated about the…

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Q: Find the volume generated by the area bounded by the y-axis, the line y=1, and the arc of y=sin x…

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Q: 1. Obtain the volume of the region rotated to the right of the y-axis and to the left of the curve x…

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Q: What is the volume formed by revolving about the x-axis the area bounded by the lines x = 1, x = 5…

A: the volume (V) formed by revolving the curve y=f(x) about the x-axis bounded by x=a, x=b (b&gt;a) is…

Q: 1/6 Find the volume of the solid obtained by rotating the region bounded by and リー2) about the line…

A: Now , we will find the  volume of the solid  obtained by rotating the region bounded by the given…

Q: 3. Find the volume when the part of the curve y = x + 1 between x = 1 and x = 2 is rotated through…

A: Here we have to find the volume when the part of the curve y=x2+1 between x=1 and x=2 is rotated…

Q: 12. Consider the region R bounded by the line y = 37 – 7x and the parabola y = 27 – x² . %3D Find…

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Q: Find the volume of the solid of revolution bounded by the circle +y = 16, and the lines 0 and

A: To find: Volume of the solid

Q: Find the volume, if an area bounded by an asteroid I = cos t y = sin³ t ve y = -/I+x ,y-axis, and…

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Q: 1. Find the area bounded by the curve y = x^2  and the x-axis and the ordinates x = 0 and x = 2 2.…

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Q: The volume of the solid that results when the region between the curve y=ex and the line y = 0, from…

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Q: 5. Find the volume generated by the areas bounded by the straight line y = x, between y = 0 and x =…

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Q: The volume of the solid generated when the region at the first quadrant bounded by the curve y = x²…

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Q: If we have a half-circle of radius r centered at 0, prove thatthe volume of the sphere resulting…

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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.