8. The region in the first octant bounded by the coordinate planes, the plane y = 1 – x, and the surface z = cos(7x/2), 0 < x < 1 |

Q: Sketch the region enclosed by the given curves. y = 6 cos ax, y= 12x² – 3 y y 4| 2 -1.0 -05 d.5 1.0…

A: Area of the Region bounded by the curve :     If f(x) and g(x) are two continuous function on [a,b]…

Q: 4. Find the centroid of the region bounded by graphs of y = 4x – x², y = 2, and r = 0.

A: As per guidelines we experts are allowed to solve one problem at a time. Please reupload the fifth…

Q: x² sin xy 14.5.8. || - dA(x, y), if D is the region bounded by æ² = "4, x² = TY, y² = ;, and D y? =…

A:

Q: 1. The solid in the first octant bounded by the coordinate planes and the surface z = 1- y – x2.

A:

Q: The area of the region bounded by the curves y = sin x, y= cos x, x = 0, x = - is 2 Select one: O a.…

A: Area of region bounded by curves.

Q: Sketch the region enclosed by the given curves. y = 7 cos(TX), y = 12x2 - 3 y y 8 6 4 -1.0 1.0 2…

A: We have to draw the graph and find out the area

Q: 1) Evaluate y)dA over a region bounded by curves xy = 6 and x + y =7. Sketch a diagram of the…

A:

Q: THE REGION BOUNDED BY 2y = x AND (x-2)² = − 4y + 12 15 REVOLVED ABOUT THE LINE Y = 4. DETERMINE THE…

A: Introduction: The washer method refers to this application of the slicing method. Because the slice…

Q: Volumes of solids Find the volume of the following solids.

A: The region is bounded by the curves, The region is shown in the graph given below,

Q: 1. Find the area of the surface z = k + xy inside the cylinder x² + y² = R² for constant R. k > 0 is…

A:

Q: - Find the volume of the solid generated by revolving about the line x = 1 the region bounded by the…

A:

Q: Let f (x) = cos x and g(x) = sin x. Find the center of gravity (x, y) of the region between the…

A:

Q: Sketch the region enclosed by the given curves. y = 6 cos(xx), y = 12x2 - 3 y 4 y 2 -1.0 -05 9.5 1.0…

A: Consider the curves  y=6cosπx,        y=12x2−3

Q: 5. D is the region in the xy-plane bounded by the curves x = cos(y), 3y 27Tx, Зу 3 — 2тх. Evaluate x…

A:

Q: 4. Finl the volume bounded by the surfaces z x2 and z 4-x2-y2.

A:

Q: The centroid of the region bounded by y = x, y = -x, and {(cos t, sin t) | st s is (circle one) (0.)…

A:

Q: Sketch the region enclosed by the given curves. y = sec2(x), y = 8 cos(x), -t/3 SxS T/3

A: Solution:-

Q: Sketch the region enclosed by the given curves. y 2 cos(7x), y = 2 sin(14x), X = 0, 14 y 2.0+ 1.5…

A: We have to find the area between the curves.

Q: 3. Suppose the following bounded region is rotated about the x-axis and creates a solid of…

A:

Q: Consider the region enclosed by the curves y = a2 +1 and y = 2r + 1:

A:

Q: ex The region bounded by the paroholm y =2, r the line y=1 in Hhe first quadrant bout the lin x=2 to…

A: .

Q: 8. Find the absolute extrema of the function f(x,y)=2x-2xy + y² over the region R. R is the region…

A:

Q: 4. Evaluate fe cosy dx + (xy – xsiny) dy where C is the boundary of the region lying between the…

A: Given  ∫Ccosydx+(xy-xsiny)dy

Q: 4. Find the volume of the solid under the surface f(x, y) = xy and above the triangular region in…

A: .

Q: The base of a solid is the region bounded by the graphs of y = 3x,y = 6, and x = 0. The…

A: Given, The base of a solid is the region bounded by the graphs of y = 3x,y = 6, and x = 0. The…

Q: 2. Find the area of the plane region bounded by y = 3x + 1, x = 1, x = 3,and the x-axis. y y = 3x +…

A:

Q: 5.5 Find the volume of the solid bounded above by the graph of f(x, y) = xy sin(x²y) and below by…

A:

Q: 12 - Which of the following is the volume of the object that occurs when the region bound by the…

A: We sketch the region using a graphing calculator  The shaded region is rotating about the y axis

Q: 1. Find the surface area of the region S in the plane z = 3x + 2y such that 0 <x < 10 and 0 < y <…

A: We have to find the surface area of the region S in the plane z = 3x + 2y such that 0&lt;=x&lt;=10…

Q: 149. sin x cos ydx + (xy + cos x sin y)dy, where C is the boundary of the region lying between the…

A: We have to find ∫c sin x cos y dx +(xy+cos x siny)dy , where C is the boundary of the region lying…

Q: 12 - Which of the following is the volume of the object that occurs when the region bound by the xy…

A: We sketch the region using a graphing calculator  The shaded region rotates around the y axis

Q: Find the areas of the regions 1. Bounded by the spiral r = 0 for 0 < 0 < T r = 0 2'2 х (п, т)

A:

Q: Consider the region bounded by the Xxy curves J 3-2x, and y=3, %3D

A: Calculating the area of the region bounded by the curves

Q: 1) Find the centroid of the region that is bounded by the line Y = 3X, the line X = 2 and the X…

A:

Q: - The region bounded by 2y = x and (x − 2)² = −4y + 12 is revolved about the line y = 4. Determine…

A:

Q: Sketch the regions enclosed by the given curves. y = 4 cos(7x), y = 4 sin(14x), x = 0, x = T/14 y y…

A:

Q: Sketch the region enclosed by the given curves. y =- y = 8x, y = x > 0 y y 6 4 3 3 2 1 1 X 2 4 -1 3…

A: Given that the curves are      y=2/x , y=8x , y=x/8 , x&gt;0 Here we have to sketch the region and…

Q: of the region bounded by the given curves. * x = 0, y = 0 b. (2,1) с. (-2,1) d. none of the choic

A:

Q: 17. (2 +y +2) dx dy dz, W is the region bounded W by x+y+z= a (where a> 0), x = 0, y= 0, and z= 0.

A: We have to solve the integral and show the graph of question 17.

Q: 4. Find the area enclosed by: a. y= sin(x) and y cos(x), x=0, x = and the y-axis. b. y=x and y =Vx.…

A:

Q: 2. Find the centroid of the region bounded by the parabola y=x² and the line y=4.

A:

Q: 13. Region bounded by: y = 4 – x and y = 0. - Rotate about: (а) the x-axis (c) y = -1 (b) у — 4 (d)…

A:

Q: Sketch the region enclosed by the given curves. x = 9y2, x = 4 + 5y2 У y 1.0- 0.5 6. -0.5 o-1.0-…

A: Given curves are

Q: (b) Use Green's Theorem to evaluate ſ. 3ysin(x)dx + 5xdy where C is the boundary of the region…

A: Solution:Given∫c3y sinx dx+5xdyFormula:∫cPdx+Qdy=∬ ∂Q∂x-∂P∂y dA

Q: 4. Calculate the volume of the solid under the plane 4x + 2y – z = 0 and above the finite region R…

A:

Q: 1. Find So(r+2y)dA, where D is the region bounded by the parabolas y r, and y=1+

A:

Q: 4/ Find the area of the region enclosed between the curves y= cos 2x , y=0, x=TT/4, x= TT/2 ? ans/…

A: Given-y=cos(2x)y=0x=π4x=π2Let consider that area of the curve is =AWe have two value of x and two…

Q: Find the absolute extrema of f(x,y) = 3x² + xy on the region bounded by the parabola y = x² and the…

A: differentiate the function partially with respect to x and y fx=6x+yfy=x Put the obtained function…

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.