The volume of the solid generated by the curve y = e", between a = 2 and a = 6 about the a – aæis is (e - e 12) cubic units 2 (e-4 + e-12) cubic units (e4 – e-12) cubic units e1² + e ^) cubic units

Q: Q3/ Find a center of mass of a thin plate of density 8 = 3 bounded by the lines x = 0, y = x, and…

A: Given region bounded by x=0 , y=x and parabola y=2-x2    in first quadrant

Q: FIND THE VOLUME OF THE SOLID FORMED BY REVOLVING THE GIVEN AREA BOUNDED BY THE LINES AND CURVES,…

A:

Q: 4. A metal plate, with constant density 2 gm/cm² is bounded by the curve y = x², the x – axis, and x…

A: Given: A metal plate, with constant density 2 gm/cm2  is bounded by the curve  y = x2  and x = 1…

Q: You create a container by rotating the curve y = 5 In(x – 5) for y = 0 to y = 5 around the y-axis.…

A: ∗ y=5 ln x-5     from y=0  to y=5⇝Density =ρ=900 kg/m3⇝ Height =1 meter       ∵ω in joules⇒ρ=m∆v…

Q: A solid is formed by revolving about the y-axis, the area bounded by the curve x³=y, the y-axis and…

A: Given: - A solid formed by revolving about the y-axis, the area bounded by the curve x3=y, the…

Q: Find the volume gererot ed lby revolving the area bounded bay the parabolic arc Vx t vy = Ja and Hhe…

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Q: Find the centroid of the solid formed by revolving about ox the area bounded by y^2=2x and the line…

A:

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

A: Given solid is obtained by rotating the region bounded x=7y2, x=7 about the the line x=7.

Q: A frustum of a cone is generated by revolving the graph of y = 2x on the interval [2, 8] about the…

A: GIVEN FRUSTUM cone generated by revolving  the graph of y=2x on interval [2,8] about x axis  we need…

Q: Find the area of the surface obtained by rotating the curve y = 3x2 from point (4, 48) to the point…

A: Let's find.

Q: Find a center of mass of a thin plate of density 8 = 6 bounded by the lines y=x and x = 0 and the…

A:

Q: 4.Find the volume of solid generated by revolving the Vosl regions bounded by the curve y = cos(-)y,…

A:

Q: Find the centre of mass of the 2D shape bounded by the lines y = ±1.1x between x = 0 to 2.3. The…

A: Given that y=±1.1x when x=0, and x=2.3 The density is 1.9kg m-2 The density is uniform is 3.1 kg m-3…

Q: Find the center of the mass of a thin plate of constant density & covering the region The center of…

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Q: ind the center of mass for a thin plate covering the region bounded by the parabola y=25-x^2 and…

A:

Q: The radius of a circular disk is given as 28 cm with a maximal error in measurement of 0.4 cm. Use…

A: Given Radius of circular disk r=28 cm Maximal error ∆r=0.2 cm Area of circular disk ,A=πr2…

Q: Find the mass and center of mass of the lamina bounded by the graphs of the equations for the given…

A: GIVEN y  =  4 − x2 y  =  0 ρ  =  ky for better understanding here I am ? replaced by ρ

Q: Tangent drawn from the point (4, –3,10) to the intersection curve of z = x² and z = 25 – y² surfaces…

A:

Q: Find the center of the mass of a thin plate of constant density & covering the region bounded by the…

A:

Q: find the center of mass of a thin plate of constant density d covering the given region. The region…

A: Given :               The density of plate is δ.          The region in the first and fourth…

Q: Find the volume of the solid generated by revolving the region about the given line. 27) The region…

A: 28) Given: The line is y = 1. The graph is drawn for the given curve and a line.…

Q: Create a bucket by rotating around the y axis the curve y = 3 In(x 2) from y = 0 to y = 6. If this…

A:

Q: A solid is formed by revolving about the y-axis, the area bounded by the curve x^3=y, the y-axis,…

A: Solution :-

Q: The center of the mass is located at (x, y) = (Type an ordered pair. Round to the nearest…

A: In the given question the region is bounded by the x-axis and the curve y=52cos x, -π8≤x≤π8.

Q: find the center of mass of a thin plate of constant density d covering the given region. 1. The…

A: Hey, since there are multiple questions posted, we will answer first questions. If you want any…

Q: Find the center of mass of a thin plate covering the region between The center of mass is (x, y) =.…

A:

Q: The region in the first quadrant that is bounded above by the curve y = ex - 1, below by the x-axis,…

A: Express the integral as below.

Q: Find the center of mass of a thin plate covering the region between the x-axis and 20 the curve y =…

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Q: A hemisphere has a radius of 3 cm. Draw complete with labels the cross section with equation of the…

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Q: find the volume of the solid generated by revolving each region about the given axis. The region in…

A: Given curve second quadranty=-x3below by x axisleft by the line x = -1about line x = -2

Q: Find the center of the mass of a thin plate of constant density & covering the region The center of…

A:

Q: A trough is filled with liquid of weight density 60 N/m3 and with cross section in the shape of a…

A:

Q: find the center of mass of a thin plate of constantdensity d covering the given region. The region…

A:

Q: Find the center of mass of a thin plate of constant density ô covering the region between the curve…

A: It is given that, y=5sec2x,  -π4≤x≤π4   Since the density is constant so we'll not require this to…

Q: A semi-circular lamina of redius R is bounded by the curve x2+2=4 and the x- axis. Find (a) the…

A: Given A semi-circular lamina of radius R is bounded by the curve x2+2=4 and the x-axis.

Q: find the center of mass of a thin plate of constant density d covering the given region. 1. The…

A: Given information:

Q: The altitude of a cylinder of maximum volume that can be inscribed in a right circular cone of…

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Q: The volume of the solid generated by the curve y = e¯*, between x = 3 and x = 8 about the axis is -…

A:

Q: Solid created from these conditiong limited to 0eyet fiest actant on ly Positive xy-plane

A: y=xx=y2,0≤y≤10≤x≤y2z=1-yy=1-z0≤y≤1-z,0≤z≤1V=∫01∫01-z∫0y2 dx dy dz

Q: 2. Find the center of mass of a thin plate of constant density d covering the region between the…

A: The thin plate mentioned is shown below: The region covered by plate is R=(x,y): -π4≤x≤π4 and 0≤y≤2…

Q: A 570-g squirrel with a surface area of 865 cm2 falls from a 4.0-m tree to the ground. Estimate its…

A: Consider the given question,The formula of terminal velocity is given by,

Q: Find the volume of the solid generated by revolving the area bounded by the given curve y=lnx, x=e2,…

A:

Q: find the center of mass of a thin plate of constantdensity d covering the given region. The region…

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Q: A disk of radius 3 cm has density 6 g/cm? at its center, density 0 at its edge, and its density is a…

A: Given radius of disc r = 3 cm Density at center ρc = 6 g/cm2 Density at edge ρe = 0 given density is…

Q: 9. Find equations of tangent plane and normal line of surface e -z+ xy 3at point(2,1,0). %3D

A: Given a surface fx,y,z=ez-z+xy=3. To determine the equation of the tangent plane of the surface at…

Q: Let RR be the first quadrant region bounded on the left by the yy-axis and between the graphs of…

A:

Q: A thin plate of constant density δ = 1occupies the region enclosed by the curve y = 36/(2x + 3)…

A: Given that : A thin plate of constant density δ = 1 occupies the region enclosed by the curve y =…

Q: find the center of mass of a thin plate of constantdensity d covering the given region. The region…

A: Consider the graph of the function given in the question: Here we have: The formulae that will…

Q: A trough is filled with liquid of weight density  50 N/m3 and with cross section in the shape of a…

A:

Q: Find the center of mass of a thin plate of constant density & covering the region between the curve…

A: Answer

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.