You are given a y=sqrt(36-x^2), -3≤x≤3, curve that rotates about the x-axis. What is the area of the resulting surface?

Q: Find the area of the region bounded by the line y = 2x − 5 and the parabola y = x2 - 4x

A: The objective of the question is determine the area between given line and parabola.

Q: Determine the area of the largest possible rectangle whose base is on the x-axis and the top two…

A: The given curve is y=9-x2

Q: Find the area of the region enclosed by the graphs of y= square root of x+3 ,x=-3 and y= 2

A: Answer and explanation is given below

Q: Matthew is constructing a rectangular prism with volume exactly 720 cubic inches. It will have the…

A: Given Information- Volume of the rectangular prism = 720 in3. The rectangular prism has the least…

Q: What is the area of the region defined by the inequalities: y -2x – 1

A: This question can be solved using the concept of graph of inequation to obtained the shaded area and…

Q: find the total area between the region and thex-axis. y = x3 - 3x2 + 2x, 0 ≤ x ≤ 2

A: Given function or curve,  y = x3 - 3x2 + 2x,        0 ≤ x ≤ 2 To find total area between the curve…

Q: What is the area of the region bounded by the parabola y = x2 - x - 6 and the line y = -4. Round…

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Q: There is a line through the origin that divides the region bounded by the parabola y=4x−6x2y=4x-6x2…

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Q: Find the area of the region in the first quadrant that is enclosed by the coordinate axes and the…

A: Now the diagrammatic representation of the area is,

Q: 2. Find the area of the region enclosed by the parabola y = 2x² and the line y = -x-1

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Q: Find the area of the region bounded by the graphs of the equations. x² + 8x, y = 0 y 200/3

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Q: Find the area of the region enclosed by the parabola y = 3x – x² and the x-axis.

A: The equation of x-axis is y=0

Q: Sketch the parabola and line on the same graph. y = 3x2 − 2  and  y = 2x + 6 Find the area between…

A: the given parabola is y=3x2-2 the given line is y=2x+6 we have to sketch the parabola and line on…

Q: Find the area of the region bounded by the parabola y = 4x², the tangent line to this parabola at…

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Q: Find the exact area of the region that lies beneath the curve y 4x-4, 1 < x < 6.

A: The exact area under the region of the curve is=∫164x-4dxWe know that…

Q: FIND THE AREA OF THE REGION IN THE FIRST QUADRANT THAT IS BOUNDED ABOVE BY y=sqrt(x) AND BELOW BY…

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Q: over the triangular region Cut from the * quadrant by the line x+y =1.

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Q: Find the total area of the shaded region (area constrained by curves) y = -2r4 -2

A: The area of the shaded region is given by  ∫abf(x)-g(x)dx Where a and b are limits of x f(x) and…

Q: There is a line through the origin that divides the region bounded by the parabola y = 8x- 32 and…

A: Here we have to calculate the slope of the line  It can be calculated by finding the area and then…

Q: Find the area of the region enclosed by the parabola y = 2x – x² and the x-axis.

A: Given: Find the area of the region enclosed by the parabola y=2x-x2 and the x-axis.

Q: Find the area of the region bounded by y=square root of 2x, y=3x-4, and y=0

A: Recall: Area between the curves:      If f(x) and g(x) are two continuous functions and f(x) ≥g(x)…

Q: Determine the area of the region enclosed by the curves y - 3x = 2 and 2x² - 4-2y = 0. Do not…

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Q: Find the areas of the regions enclosed by the curves and lines y2 = 4x, y = 4x - 2

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: What is the area of the region in the first quadrant bounded on the left by the graph of…

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Q: What is the area of the region bounded by the parabola y^2 = 2x and the line x-y-4 = 0? *

A: See the details solution in below

Q: Find the area between the curves -4x + y = 16 and -2x2 = -y+ 10.

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Q: Find the area of the region bounded by the line y = 4 - 2x and the coordinate axes.

A: Given query is to find the area bounded by the line.

Q: Find the surface area of the portion of the half ball with radius which cuts off by the cylinder x2…

A: Concept: The surface area of the half ball is given by: A=∬1+∂z∂y2+∂z∂x2dA Where ∂z∂y, ∂z∂x is the…

Q: Find the area between the curves. y = x4/3, y = 2x1/3

A: y = x4/3, y = 2x1/3

Q: y = e²x and x - 2y + 5 = 0

A:

Q: Find the area of the region in the first quadrant that is enclosed by the coordinate axes and the…

A:

Q: Find the exact area of the region that lies beneath the curve y = 8x-4, 1 < < 6.

A:

Q: How many square units is the area of the region bounded by the two curves y = x^2 - 4x and y = x^3 -…

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Q: The construction firm where you are working as an engineer plan to build a tunnel whose arch is in…

A: The arch of the tunnel is in the shape of a parabola.Let road be the x-axis And given tunnel is 12m…

Q: Find the area of the region enclosed by the parabola y = 8x – x² and the x-axis.

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Q: Find the area of the region bounded by the semicircle with the equation y = √(4- (x + 2)^2 ) + 1 and…

A: Given region is bounded by curves, y=4-x+22+1y=x2+4x+1

Q: Find the equation of a horizontal line that equally cuts the area bounded by the curves 2y=x^2 and…

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Q: What is the area of the region bounded by the parabola y = x^2 and the line y = x?

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Q: Find the area of the region between the x-axis and the curve .3 y = x³- 4x - 2 < x<2 ?

A: Let us first plot the graph of y=x3-4x, -2≤x≤2.

Q: Suppose you build an architectural model of a new concert hall using a scale factor of 55. How will…

A: According to question given that Build an architectural model of new concert hall using a scale…

Q: Find the area between the curves -16 = 4x- y and -10 = 2x-y.

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Q: Find the area of the region in the first quadrant bounded by the circle (x - 1)² + y² = 1, and the…

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Q: Determine the enclosed area by the curve 9x² + 25y² - 225 = 0

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Q: A rectangle has its two lower corners on the a-axis and its two upper corners on the curve y = 64 –…

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Q: = 4x y = 2x – 4

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Q: Find the areas of the regions enclosed by the lines and curves y2 - 4x = 4 and 4x - y = 16

A: Consider a curve: y2-4x=4……1   and line: 4x-y=16……2

Q: Find the area of the region bounded by the curves, y = -6, y = 6, the y – axis and the parabola y2 -…

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Q: Determine the area between the curves x 2 y2 and x + 15 y = 8. -2 -4 -6 -8 -10 -50 50 100 150 200…

A: This question is based on application of integration.

Q: Find the area of the shaded region between y =x2-4 and y =2x2+x-6.

A: use vertical strip to get limits

Q: Find the area of the region bounded by the curves, y = -6, y = 6 , the y – axis and the parabola y2…

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.