A frustum of a cone is generated by revolving the graph of y = 2x on the interval [2, 8] about the x-axis. What is the area of the surface of the frustum?

Q: Find the area of the surface generated by revolving the semicircle y = √1 − x about the x-axis over…

A: Given that, y=1-x. dydx=121-x-12·-1=-121-x 1+dydx2=1+-121-x2=1+141-x=1+14-4x=4-4x+14-4x=5-4x4-4x

Q: The area of the region bounded by y = v9 – x² , the x-axis and the line y=x in the first quadrant…

A: The area between the curves y=9-x2, y=x, x=0 :The area between curves is the area between a curve fx…

Q: The area of the region bounded by the two curves y = x²and y 25 is Square Units

A:

Q: Find the area enclosed by the closed curve obtained by joining the ends of the spiral r = 80,0 < 0 <…

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Q: Find the area enclosed by the closed curve obtained by joining the ends of the spiral r = 30,0 < 0 <…

A: Given, r=3θ,  0≤θ≤5.4

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

A:

Q: Find the area bounded by the parabola x = 8+2y-y², the y-axis, and the lines y = -1 and y = 3.

A:

Q: 6. Find the area of the surface generated when y = v4x + 6 is revolved about the x- axis on the…

A: 80π

Q: Determine the area enclosed by the curve 2x² + 2y² - 2x + 6y - 3 = 0

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Q: The area of the region enclosed by the curve 4x2+25y²=50 is:

A:

Q: The area of the region bounded by the two curves y = x and y = 64 is Square Units

A:

Q: Find the area of the region bounded by the parabola y = 3x2, the tangent line to the parabola at (3,…

A:

Q: Find the area of the curve bounded by the curves y=x* and y=3x+4.

A: We have to find th: e area of the curve bounded by the curves y=x4 and y=3x2+4.…

Q: The area of the region bounded by the two curves y = x“ and y = 4 is

A:

Q: The area of the region enclosed by the parabola y = 2 - x? and the line y = -x is :

A:

Q: 7. Find the radius of gyration of a plate covering the region bounded by y3,x 2, and the x-axis with…

A: Formula used:Radius of gyration, moment of inertia and area under curve with reference to y axis is…

Q: rea of the region enclosed by

A: we have to find the area of the region bounded by the curve, y=2-x2 .....(1) and the line y=-x

Q: The area of region bounded by the parabola y? = 4x and the line %3D y = 2x – 4 is -

A: We have to find the area of the region bounded by the parabola y2=4x and the line y=2x-4

Q: Find the area enclosed by the closed curve obtained by joining the ends of the spiral r = 30, 0 < 0…

A: According to the given information, it is required to find the area enclosed by the given curve.

Q: Find the area of the region bounded by the parabola y = 2x, the tangent line to this parabola at (4,…

A: Definition used -              Equation of a tangent line -                  (y-y1)=f'(x1)(x-x1)…

Q: The area of the region bounded by the curve y = a° – 3x? – x + 3 and y = 0 is

A:

Q: Find the area of the propeller-shaped region enclosed by the curve x - y3 = 0 and the line x - y =…

A: x-y3=0  &amp;  x-y=0⇒y3=x  &amp;  y=x⇒y=x13  &amp;  y=x Now the diagrammatic representation of the…

Q: Find the area of the region bounded by the parabola y = x², the tangent line to this parabola at (1,…

A: Given data: The equation of the parabola is y=x2. The given point is (a, b)=(1, 1). The slope of the…

Q: Find the area of the propeller-shaped region enclosed by the      curves      x - y^(1/3) = 0 and x…

A: First we have to find where the curves intersect. Set x equal for those curves and solve for y.

Q: Find the area enclosed by the closed curve obtained by joining the ends of the spiral r=2θ, 0≤θ≤4.5…

A: Given that  r=2θ, 0≤θ≤4.5 To Find the area enclosed by the closed curve obtained by joiningthe ends…

Q: The area of the region bounded by the curve y= e", the x-axis,'the y-axis, and the line x 2 is equal…

A: We have to find the area of the region bounded by the curve y=e2x , the x-axis, y-axis and the line…

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

A: Find the solution below

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

A:

Q: The area of the region bounded by the two curves y = x² and y =4 is

A:

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

A:

Q: Find the area of the region bounded by the parabola y = 2x2, the tangent line to the parabola at (3,…

A:

Q: Sketch the region enclosed by the curves y = x2- 4 and y = 3x − 4, and find its area.

A:

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

A:

Q: The area of the region bounded by the curves y = 4x? 3 22 and the lines æ = 1 and x = 5 and y is

A: Here is the solution of the given problem

Q: Sketch the region enclosed by the straight line y = 4x − 4 and the curve y = x2 and find the area of…

A: Given, straight line y=4x-4  and the curve y=x2we have to sketch the region enclosed by given…

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

A:

Q: Find the area of the region enclosed by parabola y=3-x2 and the line  Y=3-2x

A: We have to find the area of the region enclosed by parabola y=3-x2 and the line y=3-2x. The point of…

Q: Find the area of the region between the curve y = 1/1 + x^2 , 0 ≤x ≤√3, and the x-axis.

A:

Q: The area of region bounded by the parabola y? = 4x and the line y = 2x – 4 is

A: In the given question, the concept of integration is used to find the area of the common region.…

Q: Find the area enclosed by the closed curve obtained by the joining the spiral r=4θ by a straight…

A: Given that, the value of r=4θ and θ∈0,1.7. It is known that, the formula for the area of the…

Q: A frustum of a cone is generated by revolving the graph of y = 4x on the interval 32, 64 about the…

A: The surface area A=∫ab2π f(x) 1+f'(x)2dx

Q: Find the area of the propeller-shaped region enclosed by the curves x - y1/3 = 0 and x - y1/5 = 0.

A: We have the curves x-y13=0 and x-y15=0. We have to find the area of the propeller-shaped region…

Q: Find the area of the region enclosed by the line y = 2x + 4 and the parabola y = 4 - x2 in the…

A: The diagrammatic representation of the area is,

Q: Find the area of the region bounded by the parabola y2 = 2x-2 and the line y = x-5 using (a)…

A: We will find out the required area.

Q: The area of the region bounded by the two curves y = x² and y = 9 is Square Units

A: Draw the both curve than find their intersection points and integrate in that interval.

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

A:

Q: The area of the region enclosed by the parabola y =2-x and the line y = – xis equal to:

A:

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.