Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the given curve about the y-axis. y = 9 – (x – 7)².

Q: Find the area of the region enclosed by the curves y = Vx and y = x. = vx %3D

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Q: Find the exact area of the region enclosed by a = t - 9t and y = 4t/2 and the y-axis. Be sure to…

A: To Find: The area of the region enclosed by x=t2-9t and y=4t1/2 and the y-axis.

Q: find the volume of the resulting solid, if the region is revolved 360° about x=-1

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Q: Please find the centroid of the region. y 1 m y = x3 1 m

A: X coordinate: 4/5 Y coordinate: 2/7

Q: Sketch the region enclosed by y = 4x and y 4x2. Find the area of the region. %3D

A:

Q: = 1 + 16 9. revolving (#1) Find the volume of the solid bounded by about the x-axis:

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Q: The region is bounded by the curve y = 6x – x² and y = x² – 2x –

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find the area of the region enclosed by the three curves y = 3z, y = 6z and y = +1 in the first…

A: Here we have to find the area inclosed by the curves y=3x, y=6x and y =2x+1 in the first quadrant.

Q: A water reservoir has the shape of a right circular cone with its circular base of radius R = 160 m…

A: General formula for volume of cone, V= (Pi* R^2 * H)/3

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.