Question 8 Calculate the area of the surface generated when the curve, y = Vx is revolved on the interval [1< y< 2]about the y - axis.

Q: Question 1 Find the area between the curves y = x and y = 3x + 2.

A: The graph is shown below:

Q: Question 12 Find the moment of inertia of the region between the parabola y = 9 - x2 and the line y…

A:

Q: cos(3t), y = 6+ sin(3t) on 0 <t <

A: Please see the explanation below

Q: QUESTION 8 Find the area of the cylindrical surface in Xyz-space where a point (X,y,z) on the…

A: Find the surface area of the cylinder in xyz-space where a point x, y, z on the surface satisfies…

Q: Question 3 ( ) Evaluate the integral 11₂ D ydA where D is the region bounded by the curves = 0 and x…

A:

Q: Find the surface area generated by revolving the curve x=y³²-y about the y-axis for 1≤ys 3/2 1/2 3

A: The surface area of any given object is the area or region occupied by the surface of the object.

Q: QUESTION 4 Find the area of the region bounded by the given curves. y=x-4x, y = 3x+8 25 a. 3 ОБ. 243…

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Q: Find the exact area of the surface obtained by rotating the given curve about the x-axis. x = a cosº…

A:

Q: Question 8 Find the area of the region bounded by the curve y=1- and the x-axis. 9 A) 0 B 4 square…

A: Given query is to find the value of the area.

Q: cos(2t), y = 4+ sin(2t) 0 <t< on 2

A:

Q: Question 2 At what value of the parameter b (b > 1) the area under the curve y = x2 on the interval…

A:

Q: Find the area between the two curves.

A:

Q: Find the exact area of the region that lies beneath the curve y = 2 sin(x), 0 < x < T.

A: The exact area of the region beneath the curve can be find using definite integrals. If fx≥0 is a…

Q: Question 2 At what value of the parameter b (b 1) the area under the curve y= c on the interval (1,…

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

Q: QUESTION 1 Find the area enclosed between the two curves y --r and = 8- 87 Oa-343/6 Ob 243/2 c. No…

A:

Q: Question 10 Find the area enclosed by the curves y = 2x √3- π ® ²-√√4-. (A) А Im 21/12-4/09/20 7x D…

A: The equation of curves are: C1: y = 11-9x2C2: y = 2 To evaluate: The area enclosed by the curves.

Q: Find the surface arca of y = (1/3)r 10<x <1 revolved about the z-ax

A: Given: The equation is y = 13x3 , 0 ≤x≤1 revolved about the x - axis.

Q: Question 10 Determine the area bounded by the curves y = ex, y=x²-1, x=-1, and x = 1.

A:

Q: Question 4. Find the area bounded by the indicated curves. y =x- 9x, y = 0

A:

Q: Question 1 Area bounded by the curves y=e", y=e", x=0 and x=In2 A 604/9 B 502/9 304/7 304/14

A: Ara of the above bounded curve is given by

Q: Find the area of the surface generated when the given curve is revolved about the given axis. y =…

A:

Q: Find the area of the surface generated when the given curve is revolved about the y- axis. y =, for…

A: Answer is optional B

Q: Question 3: Find the area between the curve y = 6 – x² and the line y = -3x + 2.

A:

Q: 3) Find the area of the surface formed by revolving the graph f(x) = ;x³ about the x-axis over the…

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Q: Question 3: Find the area between the curve y = 4 – x² and the line y = -x + 2.

A:

Q: Find the area of the region between the curve y = sin t andthe t-axis from t = 0 to t = 2π.

A: the area of the region between the curve y = sin t andthe t-axis from t = 0 to t = 2π is defined as…

Q: The area between the two curves in * the figure below is y = cos x y = sin 2x T/6 T/2

A:

Q: Question 13 Find the area of the region bounded by the curve y=1- and the x-axis. 6. A 4 square…

A: A detailed solution is given below

Q: Find the area between the curves. 4x y3e 8. x= 0, x= 3, y= 2 e y=e+ e

A:

Q: Find the area of the surface obtained by rotating the given curve about the x-a T x = 5 cos (0), y =…

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Q: and y = 1 Question 2. Find the area of the region bounded by the curves x = 1, y = 2+VI 2-VE

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Q: Find and shade the area to the left of cach positive z value. Given Curve 1. C-0.9s 2. z= 1.47

A: As per company guidelines I solved exactly three subparts of the question.thank you

Q: Question 14 Find the area of the surface that is generated by revolving the portion of the curve y=…

A: Given: y=x2⇒x= ±y Since , we are dealing with x=1 to x=2, we will take the positive value Thus, x=y…

Q: The area between the two curves in the figure below is y = cos x y = sin 2x T/6 T/2

A:

Q: Question 3 Find the area enclosed by the curves y y = 2 V1- 9x2 O V5- 9. 2n B 3 5n D 6

A: Solution is given below:

Q: Question 2 Area bounded by the curves y=e*, y=e", x=0 and x=In2 (А) 604/9 (В) 304/14 C) 502/9 304/7

A:

Q: 3. Find the area of the surface generated by revolving the graph of f(x) := sin x about the x-axis…

A: Follow the procedure given below.

Q: Find the area of the closed region enclosed by the curve defined parametrically by x = 4 cos t, y =…

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Q: Question 46 Find the volume of the solid that results when the region in the first quadrant bounded…

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Q: Question 7 Calculate the area of the surface generated when the curve, f(x) = x³/2 . x1/2 on [1,2 ]…

A: Here f(x)= x32-x123 on the interval [1,2]it is revolving about the x-axis .The surface…

Q: QUESTION 4 The area enclosed between the x-axis and the curve y=x² between x=1 and x=2 is:

A:

Q: Calculate the area between the parabola y = x² and the line y = 4 shown in Figure 3.1 below: y y = 4…

A: Intersection of parabola y=x2 and the line y=4 will be  x2=4⇒x=±2

Q: the surface area of a .17 rotating the curve y = x power 3 around the x - axis between the points…

A:

Q: The curve y = √x + 2 is revolved about the y-axis from x = 1 to x = 8, find the surfac area.

A: Here we have to find the surface area.

Q: Question 2 Consider the curves y = mx and y = x³, where m is some positive real number. Find the…

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Q: 4. Find the area of the surface formed by revolving the graph of f(x) = x² on the interval [0,…

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Q: Question (4): Find the area of the region bounded by the curves: y = cos(nx) and y = -1+ 4x?

A:

Q: O Find the area of the region enclosed by the ellipse x = a cos t, y = b sin t, 0<t< 2n

A: Since you have asked multiple questions in single request.so we will answering only first…

Q: 2. y = ln(x²-1), 2 ≤ x ≤ 3 ;y-axis

A: The given problem is to find the area of surface of the revolution of the given curve over the given…

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.