Evaluate 2x dV Over the region E bounded by the parabolic cylinders y = x2 and x = y² and the planes z = 0 and z = x + y. %3D

Q: Find the ordinate of the centroid of the region bounded by the parabola y = -x2 and the line x = 2y…

A:

Q: Calculate the area bounded by the curve obtained by the function given by y = x² - 16, and the lines…

A: The area bounded by the function y = fx, and the lines x=a, x=b and y=0 in given by A = |∫abydx |…

Q: Find the distance between the planes x + 3y – 2z = 3 and 2x - y - z = 4. %3D

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  &  x-y=0⇒y3=x  &  y=x⇒y=x13  &  y=x Now the diagrammatic representation of the…

Q: Find the area bounded by y = (11 – x)7, the lines 3x=2, x=10, and the x-axis

A: We have to find the area bounded by the curves.

Q: Find the centroid of the triangular region cut from the first quadrant by the line x + y = 3.

A: We will find the x and y-intercept of the triangle.  To find x-intercept we plug y=0 and find x…

Q: Find the area of the region included between the parabolas y² = 4(p+1)(x + p + 1), and y² = 4(p² +…

A: As per the question we are given two parabolas defined as : P1  :  y2 = 4(p+1)(x+p+1) P2  :  y2 =…

Q: Calculate the area of the region that lies between the line y=-1 and the parabola y = x²-6x-1,

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Q: Find the area of the region bounded by the graphs of the equations. y = 7x2 + 1, x = 0, x = 2, y = 0

A:

Q: 6. Find the area of the region in the first quadrant which is bounded by y = 3x -8 and y=4-x a) 20/3…

A:

Q: Find the center of gravity of the region between the graphs of y = x + 2, y = -3x + 6, and y =…

A: We have to find the center of gravity of the region bounded by

Q: Shade the area of the region bounded by the parabola, x 2+p2-2(p+7)x-5y+59 + 14p 0 and the straight…

A: Equation of the parabola: x2 + p2 -2p+7x - 5y + 59 + 14p = 0               (1)Equation of lines:x =…

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.