Find the volume of the solid of revolution bounded by the circle (x)^2+(y)^2=36,and the lines x=0,x=4,about the x-axis.

Q: Determine the volume of the rotating object that occurs if the area of ​​the curve y1 = - x2 + 4 and…

A:

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

A: To Find: The surface area of the portion of the half ball with a radius a which cuts off by the…

Q: Calculate exactly the volume of the solid obtained by rotating the area delimited by y=(x-2)^2 and…

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

A: 80π

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

A: The equation of a ball with radius a is x2+y2+z2=a2. The surface area of the function z=fx,y over…

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: The centroid of the area bounded by the parabola y^2 = 4ax and the line x = p coincides with the…

A: Please see the attachment

Q: find the lateral (side) surface area of the cone generated by revolving the line segment y=7/3x, 0…

A: What is Solid of Revolution: A solid can be formed by revolving a region in two dimensional…

Q: (i) Verify the Lagrange's mean value theorem for the function f(x) = x-sin x in every interval, and…

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

Q: Consider a closed storage tank S with walls given by the curved surfaces x = y^2; z ≥ 0 and x =…

A: (a) The base of the tank is bounded by x=y2 and x=2-y2. So, the point of intersection will be,…

Q: EX- Find the area of the surface generated by rotating the 1 portion of the curve y= (x²+2)³ between…

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Q: Find the area of the plane x−2y+5z=13 cut out by the cylinder x^2+y^2=9

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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.