Compute the surface area of revolution about the x-axis over the interval [3, 5] for y = 2x + 4.

Q: Find the surface area of revolution about the y-axis of y = 3 – 3x over the interval 0 < x <1

A: Given

Q: Find the surface area of revolution about the x-axis of y = 3x + 4 over the interval 1 < x < 2

A: Answer

Q: Find the surface area of revolution about the x-axis of y=3sin(5x)y=3sin(5x) over the interval…

A: I am attaching image so that you understand each and every step.

Q: Set up an integral to find the area of the surface that is obtained by rotating the curve y = V4 –…

A: Here, y=4-x2, 0≤x≤1 is positive and has continuous derivative on 0≤x≤1. So, the surface area of…

Q: compute the surface area of revolution about the x-axis over the interval. y= x3, [0, 2]

A:

Q: Determine the surface area generated by revolving the curve y=1/3 x³ over the interval (0,2), about…

A: The given curve is y=13x3  on 0, 2. This implies that, dydx=x21+dydx2=1+x41+dydx2=1+x4y1+dydx2=13x3…

Q: Find the surface area of revolution about the x-axis of R.

A: Given curve y=2x, 2.3≤x≤4.2 We have to find the surface area of revolution.

Q: Find the surface area of revolution about the y-axis of y=6x+3 over the interval 0 ≤ x ≤ 3

A:

Q: Find the surface area for the solid of revolutic -1< x<1 about the x-axis.

A:

Q: Compute the surface area of revolution about the x-axis over the interval 0,11 for y = e , (Use…

A:

Q: Compute the surface area of revolution about the x-axis over the interval [3,6] for y = 4x + 4. (Use…

A:

Q: Find the surface area of revolution about the x-axis of y=5x+7 over the interval 0≤x≤3

A: S=∫2πydsds=1+dydx2

Q: Compute the surface area of revolution about the x-axis over the interval [0, 1] for y = e (Use…

A: Solution is given below

Q: Compute the surface area of revolution about the x-axis over the interval [2, 4] for y = 4x + 5.…

A:

Q: Find the surface area of revolution about the x-axis of y 4x +7 over the interval 0 < r<3

A:

Q: Compute the surface area of the solid obtained by revolving the region between the x-axis and the…

A:

Q: Compute the surface area of revolution about the x-axis over the interval [0, n] for y = 6 sin(x).

A:

Q: Find an integral for the area of the surface obtained by rotating y = √25-x, 9 ≤x≤ 16, about the…

A: To find an integral for the area of the surface obtained by rotating the below equation about the…

Q: Find the surface area of revolution about the x-axis of y = 2x + 7 over the interval 0 <x <1

A:

Q: 5. Find the surface area when the curve C = {(x,y): 0 < x < 2, y² = 2 – x} about the x-axis.

A: Surface area

Q: 7) Set up and evaluate the definite integral for the area of the surface generated by revolving y…

A:

Q: Set up the integral for the surface area of the solid created by revolving y= Vx 1< x <8 about the…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find the surface area of revolution about the x-axis of y=4x+3 over the interval 2≤x≤5

A:

Q: The base of a lamp is constructed by revolving a quarter circle  y = (2x-x^2)^0.5  around the…

A:

Q: Compute the surface area of revolution about the x-axis over the interval [0, 1] for y = 4x³. (Use…

A: In this question we have to find the surface area of the revolution about the x-axis.

Q: Find the surface area of revolution about the x-axis of  y= 4sin(4x), from x is greater than or…

A: Equation of curve is y= 4sin(4x) The interval is 0≤x≤π2

Q: Find the surface area generated by y = x³; x = 0 and x = 3 and is revolved on x-axis.

A:

Q: Compute the surface area of revolution about the x-axis over the interval [8, 5e] for y = x² -…

A:

Q: Find the surface area of revolution about the x-axis of y=7x+1 over the interval 1 ≤ x ≤ 3

A: The given equation is y=7x+1 over the interval 1≤x≤3. Calculate the surface area of revolution about…

Q: Find the surface area of revolution about the x-axis of 6x +1 over the interval 2 < z < 3

A: Given y=6x+1 over the interval 2≤x≤3

Q: How far is the centroid of the area boundded by the curves y=e^x, y=e^-x, and x=1 measured from the…

A: We have to find the distance of centre of mass from y Axis  So , find only x coordinate of centre of…

Q: Compute surface area of revolution about the x-axis over the interval (0, pi) for y= 6sin(x)

A: Surface area of curve revalue aroundx-axis is given by,S = ∫ab2π y 1+dydx2 dxa,b is the interval.

Q: Compute the surface area of revolution about the x-axis over the interval [3,6] for y = 2x + 5. (Use…

A:

Q: Compute the surface area of revolution of f (x) (x + 1)z about the x-axis over 3 [0,1]

A:

Q: Find the abscissa of the centroid of the region between the parabola y = 6 − x2 and the line y = 1 −…

A:

Q: Find the surface area of revolution about the x-axis of 3 sin(7x) over the interval 0 < z <

A:

Q: Find the surface area of revolution about the x-axis of y = 5 sin(4x) c

A:

Q: Find the surface area of revolution about the x-axis of y 6x + 3 over the interval 2 < x < 5

A: In the question the curve given is - y=f(x)=6x+3 , 2≤x≤5 We need to find Surface area of revolution…

Q: Find the abscissa of the centroid of the region between the parabola y = 9 − x^2 and the line y = 1…

A:

Q: Compute the surface area of revolution about the x-axis over the interval [0,1) for y = 4x'. (Use…

A:

Q: compute the surface area of revolution about the x-axis over the interval. y = (4 − x2/3)3/2, [0, 8]

A:

Q: Find the surface area of revolution about the y-axis of y = 5x + 1 over the interval 0 < x < 3

A:

Q: Find the surface area of revolution about the x-axis of y = 2x + 6 over the interval 2 < x < 5

A:

Q: Compute the surface area of revolution about the x-axis over the interval [0, 1] for y = e-9x.

A: Given: y=e-9x and 0, 1 To find the surface of revolution about the x-axis on 0, 1 The formula for…

Q: compute the surface area of revolution about the x-axis over the interval. y = x, [0, 4]

A:

Q: Find the surface area of the curve f (x) = x over [1,2| rotated .3 3 about the – axis -

A: The revolution of the curve y = f(x) around the x-axis is: S=2π∫abf(x)(f'(x))2+1dx

Q: Set up and evaluate the definite integral for the area of surface generated by revolving the curve…

A:

Q: Find the surface area of revolution about the x-axis of y=2x+4 over the interval 2≤x≤3

A:

Q: Compute the surface area of revolution about the x-axis over the interval [3, 6] for y = 4x + 5.…

A: The equation of the curve is given by y = 4x+5 Formula Used: S = 2π∫36y1+dydx2dx To evaluate: The…

Q: Find the surface area generated by rotating y=(1/3)x^3 bounded by y=0 , x=0 , and x=9 about the the…

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.