Find the surface area of revolution about the x-axis of y=5x+7 over the interval 0≤x≤3

Q: Find the area of the region between x=0 and x= 2, above the x-axis, and below the curve y=4x−x3.

A: Given: y=4x−x3     To determine: Area under the curve from x = 0 to x = 2.

Q: Find the total area of the region between the curve and the x-axis. y= -x +9, 0 sxs5 98 O A. 3 O B.…

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Q: 3. Find the area of the region in the first quadrant that is bounded by y=Vx , x-axis and y=x-2. |

A: 3) To find the area under the curve in first Quadrant

Q: Find the area of the region between y = 5x“ and y = x- + 6.

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Q: Find the total area of the region between the curve and the x-axis. 24) y = x2(x- 2)2; 0sxs2 15 A) -…

A: The graph of the bounded region is as shown above. As shown draw a stipe parallel to y-axis. So, y…

Q: Find the area of the region above the curve y = x^2 - 6, below y = x, and above y = − x.

A: Given region bounded above by  y=x2-6  and y=-x  and bounded below by y=x

Q: I- Find the area of the region bounded from the right by the curve x 4-y, from the left by the line…

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Q: Find the area between the curves. x = 0, x = 3, y = 2e3x, y = e3x + e6

A: To find the area between the curves, f(x)=2e3x and g(x)=e3x+e6, use the formula, A=∫ab[g(x)-f(x)]dx.…

Q: Find the area of the “triangular” region bounded on the left by y = √x, on the right by y = 6 - x,…

A: Concept: The simplest area calculations are for squares and rectangles and to find the area of a…

Q: Find the area between y = x^2 + 4, x = 1 and y = 0.

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Q: Find the total area of the region between the curve and the x-axis. 2) y = (x + 1/x; 4 sx s 9

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Q: 2. Determine the area of the region bounded by the curve y = x³ – x2 – 2x, and а. the x-axis b. the…

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Q: Q- Find the area of the region bounded from the right by the curve x = 4 - y? ,from the left by the…

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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 total area of the region between the curve and the x-axis. y = 2x +7;1sxs5 O 26 O 52 O 18 O…

A: Given query is to find total area of region bound by the curve with x axis.

Q: Find the total area of the region between the curve and the x-axis. y= 2x-x, 0sx s2 O A. 3 O B. 3.…

A: Explanation: Given that: y=2x-x2 Concept: The area under the curve  A=∫abfxdx here a=0b=2

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

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Q: Q2/ Find the area of the region in the first quadrant bounded on the left by the y-axis, below by…

A: The total area of the bounded region in the first quadrant is 2.5 units.

Q: Find the area between y =x+2 y = -2x+4 y = (2-x)/2

A: equation  at x=0 at y=0 y=x+2 y=2 x=-2 y=-2x+4 y=4 x=2 y=(2-x)/2 y=1 x=2 here we need to…

Q: Find Mx and My for the first-quadrant area bounded by y2 = 4x, the x-axis and x = 4. (ans: 16,…

A: Given the first-quadrant area bounded by y2=4x, the x-axis and x = 4.

Q: Find the total area of the region between the curve and the x-axis. 13) y = x2(x - 2)2; 0 s x s 2…

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Q: Find the area enclosed between the curve y = 9- x squared and line y = x + 7 A 2.5 B 3.5 4.5 5.5

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Q: Find area of the region under the curve and above the x-axis for  2≤ x ≤4.…

A: To determine :  The area of the region under the curve y = 8x2 ex -1x2 above the x - axis for…

Q: Find the area bounded by the curve y=x^2 and the x-axis and the lines x=1 and x=3.

A: Given: y=x2, x=1, x=3, and x-axis or y=0. So, from the given curves the bounded region is as shown…

Q: The enclosed area between y= 2 x and y= 6/x is evaluated by

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Q: Find the area of the “triangular” region bounded on the left by x + y = 2, on the right by y = x2,…

A: Graph the given equations first.We have to find the area of the shaded region

Q: What is the area of the region between y=x²-2x-3 and the x-axis from to 6? x=0

A: Area bounded by the curve fx=x2-2x-3 and x-axis on interval 0, 6

Q: y y = x 1 y = x V1 – x2

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Q: 7. Find the area of the region bounded above by the line y 3, below by the graph of y VT, between…

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Q: What is the area of the region between y = x - 2x- 3 and the x-axis from X = - 2 to X = 0?

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Q: Find the area of the region in the first quadrant bounded on the left by the y-axis, below by the…

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Q: can i get step by step help please

A: We have given y = 2x – x2; 0 ≤ x ≤ 2

Q: Find the area of the region between the curve y = 3 - x² and the line y = 1 -x from x = 0 and x = 2.…

A: The region between the curve y=3-x2 and the line y=1-x from x=0 to x=2

Q: Find the total area of the region between the curve and the x-axis. 7) y = 2x - x2; 0 sx<2

A: Given, The curve  y = 2x-x2   ;  0≤x≤2 We have to find the area of region between the curve and the…

Q: Find the area bounded by y=2x-x^2 , the x – axis, and the lines x =0 and x= 4.

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Q: Find the area of the shaded region. y 4 2 y=V x ((1, 1) X= 8 y = X 4 6 8 1,

A: The region is bounded by the graphs,y=x3 and y=1x from x=1 to x=8

Q: Find the area enclosed between the x-axis, the curve y= (x-15)(7-x)(x+12) and the lines x=-12 and…

A: We have to find the area enclosed between the x-axis, the curve y=(x-15)(7-x)(x+12) and the lines…

Q: 2. Find the area bounded by the line x – 2y + 10 = 0, the x- axis, the y – axis and x 10.

A: The red line is x=10 and the blue line is given line i.e. x-2y+10-0 Given x-2y+10=0This can be…

Q: Find the area between the curve and the x axis over the indicated interval. Y=4-x square; [-2,2|

A: Given: Y=4-x2 to find out: area between the curve and the x -axis over the interval [-2,2]

Q: Find the area enclosed by {x=t3/2+t+6 & y=-t2+5t-4} and the x-axis

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Q: Find the area of the region above the curve y = x2-6, below y= x, and above y=−x.

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Q: What is the area of the region between y =x-2x-3 and the x-axis from x=0 to x-9?

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Q: 3. Determine the area above f(x) = x² + 2x + 3 and below the line y = 11.

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Q: Find the area of the region in the first quadrant bounded on the left by the y-axis, below by the…

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Q: Find the area of the region between y=x1/2 and y=x1/4 for 0≤x≤1.

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Q: 3. Find the area of the region bounded by the curve y = Vx – 1, the y - axis and the lines y=1 and…

A: Simplify the equation y=x-1 to obtain the expression of x. y=x-1y2=x-1x=y2+1 Draw the graphs…

Q: Find the total area of the region between the curve and the x-axis. y = 2x +7;1sxs5 52 26 9. O 18

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Q: What is the area of the region between  y=x^2 -2x-3 and the x-axis from x=0 to 6?

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Q: Find the area of the region bounded above by y = x + 6, bounded below by y = x², and bounded on the…

A: We need to calculate the intersection points of the given curves. So,…

Q: 2. Find the area of the region between the curve, x = y² + y −6, y- axis and y=0; y = 3.

A: we need to find the area bounded by the given curves.

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.