-y = h -X- Probs. 9–18/19

Q: Find the area of the region enclosed by the positive x-axis and spiral r = 4u/3, 0<= u <=2pai.…

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Q: 2. Find the area bounded by a curve x = y - 2y? - 3y and the x- axis 3. Find the area bounded by a…

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Q: 3.5 3.0 2.5 2.0 1.5 y 10 0.5 0310 15 20 25 30

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Q: Find the the surface area of of the indicated surface The portion x +3y+z = 6 in the first octant.

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Q: Find the area of one side of the "winding wall" standing orthogonally on the curve y = x², 2sxs4,…

A: Given curve is: y=x2, 2≤x≤4 The curve on the surface fx,y=x+y To find the area of one side of the…

Q: Find the centroid of the region. NOTE: Enter the exact answers. (T, 9) (?, ?) y = x5 1

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Q: Find the average height of the paraboloid z = x +y over the square 0sxs4, 0<ys4. The average height…

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Q: Find the area of the region enclosed by the curves. x2 y = x? - 4| and y = + 4 The area is

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Q: Find the area enclosed by the given curves. y 2x-x, y-2x-4 37 34 OB. 3. 31 32 3 D.

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Q: Find the area of the part of the cylinder x+z= 49 that lies above the square with vertices (0, 0).…

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Q: 2) Find the area bounded by the curve y=x² + x + 4, the x-axis and the lines x = 1 and x = 3. (Draw…

A: Given information: The curve given is y=x2+x+4, x-axis and the lines x=1 and x=3. The area of our…

Q: Find the centroid of the region. NOTE: Enter the exact answers. |(T, 9) (?, ?) y = x10 1

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Q: Find the area of the region cut from the first quadrant by the cardioid r = 1 + sin theda.

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Q: Find the area of the cardioid r = 2 + 2sine, 0 < 0 < 2n. (show all necessary details)

A: See the details solution below

Q: Find the centroid of the region. NOTE: Enter the exact answers. (ï, 9) = |(?, ?) y = x? 1

A: Explanation of the answer is as follows

Q: EM: he the centroid of the first quadrant area bounded by the parabola y=4-x²? (3 5/8)

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Q: Find the areas below. b) The area bounded by the parabolas y = 6x - x² and y = x² – 2x. (Round…

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Q: Find the area bounded by the parabola x=8+2y-y², the y-axis, y=-1, and y=3 A) 92/3 s.u. B) 92/4 s.u.…

A: A detailed solution is given below.

Q: The signed area between the r-axis and the curve y

A: 8.    ∫-181+xdx + ∫1e421xdxLet u = 1+x    du = dx∫09udu + ∫1e421xdx23u32|90 + ln(x)|e42123(932 - 0)…

Q: Find the area enclosed by the x-axis and the curve y = -x² + 9. ... 32 А.) В.) 18 s.u. s.u. C.) 36…

A: Topic = Area Area = 36 s.u.

Q: Find the centroid of the region. NOTE: Enter the exact answers. x, y) = |(?, ?) y = V49 – x²

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Q: Find the area inside the curve r=6+costheta

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Q: Find the area enclosed by the x-axis and the curve y = -x2 + 9. A.) * 32 s.u. В.) 18 s.u. C.) 36…

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Q: Find the centroid of the region. NOTE: Enter the exact answers. (T, 9) (?, ?) y = x? 1

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Q: Find the centroid of the region bounded by the graphs of y = x? and + y = 56. NOTE: Enter the exact…

A: The given curves are y=x2 &amp; x+y=56. The region bounded by the curves is:

Q: Evaluate B) Find the area between the parabolas x = y? – 1 and x = 2y? – 2

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Q: Find the centroid of the region. NOTE: Enter the exact answers. (T, g) (?, ?) y = x10 1

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Q: 2. Find the centroid of the area in the first quadrant under the curve y = 4 – x2. Answer:

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Q: Q5 / Find the area of the triangular region in the first quadrant bounded by the x-axis and the…

A: We have to solve given problem:

Q: Determine the centroid of the area shown relative to the x-And y-axis.each small square is 2cm

A: Let divide the given figure into three parts.

Q: Find the area of the shaded region. y 14 (1,5e) 12 1아 y-5e/ 8 4 y = 5 xe -1.0 -0.5 0.5 1.0 1.5 2.0…

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

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Q: Find the centroid of the region. NOTE: Enter the exact answers. (7, 9) (?, ?) %3D y = 23

A: The expression for the centroid is: x¯=1A∬xdydx &amp; y¯=1A∬ydydx   Where; Area=A=∬dydx   From the…

Q: Find the centroid of the region. NOTE: Enter the exact answers. (ī, 9) (?, ?) y = /49 – x²

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

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Q: Find the area bounded by the parabola x=8+2y-y², the y-axis, y=-1, and y=3 A 92/6 s.u. B 92/4 s.u.…

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Q: Find the area between the curves. x = -5, x=2, y = 2x² +5, y = 0 The area between the curves is…

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Q: Determine the area enclosed by the curve r² = 4a²cos3θ a. 4a² b. 8a² c. 16a² d. a²

A: To find the area enclosed by the curve r2=4a2cos3θ

Q: Find the centroid of the region bounded by the graphs y = x2 and y = x + 30. NOTE: Enter the exact…

A: Given region is y=x2 and y=x+30

Q: b) Find the area bounded by the – axis, y = x and y = 2 – x.

A: Area bounded by the curves

Q: a) Find the area of the region enclosed by the curves y = 12 – x² and y = x? - 6. Answer: A =

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: y 6" 2" 4" 3" - x 4" -6" Using the figure above, calculate the following 1. Total area of the…

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Q: Determine the coordinates of the centroid of the area x by the curve x2 = -(y - 4). the x-axis and…

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Q: Find the area of the shaded region below. yA x= y? – 4y (-3, 3)– x= 2y – y? Area =

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

Q: Find the area of the region enclosed by y = e*, y = 2, and the y-axis. a. 2ln2 - 2 O b. 2ln2 - 1 C.…

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Q: Find the centroid of the region bounded by the curves y= x-4 and y = 2x - x. Note that the area of…

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Q: Find the area of the region that lies inside the first curve and outside the second curve.…

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

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Q: Find the centroid of the region. NOTE: Enter the exact answers. (x, y) (?, ?) = y y=x8 1 8

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Q: The radius of gyration of the area shown about the x axis is: Y 4 2. 3.

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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.