R is the region bounded by the functions f(x) = x + 2 and the x-axis and the lines x=1 and x=4. Represent the volume when R is rotated around the line x=4. Volume = dx Use pi for "T" and sqrt(x) for "T"

Q: Find the equation of the vertical line that divides the area of the region R bounded by 1 y = 20x2…

A: Identify the limits of integration from the given region, to calculate the area of the region. Here,…

Q: Find the area of the region between the functions y = (x – 5)3,y = x – 5.

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Q: Ris the region bounded by the functions f(x) = x + 2 and the x-axis and the lines x=1 and x=3.…

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Q: Find fne volume og the sohid öL taimed by rotading he region giren by y=*, yz0, x=, and =2 albant…

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Q: Find the area bounded by the curves -x + y² = 8, x = -2y and y = -2.

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Q: Q1: Find the area of the region between the curve y x-3x and the line y = x.

A: Let us consider the curve y=f(x) and y=g(x) between the interval [a,b] The area under the curve is…

Q: Find the distance between the point (-1,2) and the line with x-int 1/3 and y-int 3/4.

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Q: A metal casting is done with the limits of x-y = 4 and x = y2 - 4y+ 4, which is revolved around the…

A: Metal casting limits is x-y=4,   x=y2-4y+4 (about x -axis) Now v=π∫x1x2fx2-gx2dx

Q: Let the region R be the area enclosed by the function f(x) = 2x³ , the horizontal line y = –3 and…

A: Given the region R be the area bounded by fx=2x13,y=-3,x=0,x=3. Visualize the solid: Each…

Q: Find the domain and range of z= f(x,y)= ln(y-x^2). A. Graph the region in xy-plane that represents…

A: Domain is the set of all the possible inputs of the function. Range is the set of all possible…

Q: Find the area of the region between the curves y = x and y = x². Area between curves =

A: It is given that,  y1=x and y2=x2 Therefore,                    x2=x⇒x2-x=0⇒x(x-1)=0 ∴  x=0,1…

Q: Find the area of the shaded region. y 3- 2 X = y' - 5 y = 1 x = e -6 -4 -2 2 4 y = -1 2

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Q: Find the area of the region between the curves y = x + 1, y = 9 – x², x = -1, and x :2. %3D Area…

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Q: y = x? - x - 12, y = 0, x = -3, x = 3 y 10 10 10 10 5 -4 2 -4 -2 4 2 4 -5 - 10 10 -10 -10 Find the…

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Q: R is the region bounded by the functions f(x) = x + 2 and the x-axis and the lines x=2 and x=4.…

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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.