2)Evaluate ex dA , Ris bounded by y = x2,y = 1

Q: calculate th integral SSo(x+y) dydx where D is th reigon that deter mined in thees Curves : Y = x, Y…

A: Solution is given below:

Q: Let R be the region bounded by the curve y = r and the line y = 2x. Use inequal- ities to describe R…

A: In this question we have to describe the area of region by using vertical cross section

Q: Evaluate the line integral ſc 2y dx + 6x dy where C is the straight line path from (4, 1) to (6, 5).…

A: Given query is to find the integral.

Q: Find the volume of the 'ice-cream' that is bounded by x2 + y2 + z2 : = 35 and the upper cone z2 =…

A: The given problem is to find the volume of the ice cream that is bounded by given surfaces. Given…

Q: what is the limited area between x = 4y^2-3 and y^2 = x curve Br^2?

A:

Q: YA y= /(x) 0. C

A: Topic- area under the curve

Q: Evaluate the line integral x'z ds, where C is the line segment from (0, 5, 2) to (4, 6, 5).

A:

Q: 2)Evaluate || dA ,Ris bounded by y = x2 ,y = 1 et2 R. 3)Evaluate | Vy2 + 1dA, Ris bounded by x = 4-…

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

Q: Compute area of the region bounded byx2+ (y−1)2= 9 andy=x+ 1 and the (horizontal) liney= 1 (we…

A:

Q: Find the area bounded by the following curve and line: 4y = x² - 2lnx, y = 0, x = 1, x =4

A: Here we have to find the area bounded by the given curve and lines    4y=x2-2lnx, y=0, x=1,x=4

Q: Find thearea bounded by x=y^2 and y=-x^2

A: The region is bounded by x=y2 and y=-x2

Q: Let R be the region bounded by the curve y = x and the line y = 2x. Use inequal- ities to describe R…

A: To describe: The region R using inequalities in terms of its vertical cross-sections. Calculation:…

Q: The region R is bounded by y 4 %3D and y = x +3. -

A:

Q: A region in the xy-plane is bounded by y = 2x + 2, X = y + 2, y = -2, 2 y = 2. and

A: Given curves are y=2x+2 and x=y22+2 The limits are y=-2 and y=2 We isolate x from the first curve,…

Q: Find the area bounded by the curve ya O 16 square units O 10 square units 4 square units O 8 square…

A:

Q: Find the area of the reglon bounded by the graphs of the equations. y = 5x +5, x = 0, x = 2, y = 0

A: Required area is…

Q: The area bounded by the curve y = 10x and the lines z = 7,x = 11 and a – axis is O 850 square units…

A: Given y=10x,x=7,x=11 and x-axis  Area= integral a to b f(x) dx  Let y=f(x)=10x then find area…

Q: A region is bounded between x = 0, y = 1, x = 1, and y = (x-1)^2+1. What is the area of this region?

A:

Q: he volume bounded by the function_z = f(x, y) = xy√x² - y² <10 and 0≤ y ≤8. over

A:

Q: End the are of the ryin bounded by yox: 5x* +. baunded by y=x'r Sx' the x-axis.

A: In this question we will use basic of calculus i.e application of integration for finding area…

Q: Start with the area bounded by y = x^2, y=0 and x=2, then rotate around the line x=3

A:

Q: Find the volume of the 'ice-cream' that is bounded by x2 + y2 + z2 = 51 and the upper cone z2 = 3x2…

A:

Q: ·bounded by x² + 2y = 4 and and determine: Sketch the area x+y+2=0

A: 1st we will find point of intersection of lines and curve to identify bounded region . Then will…

Q: Find the volume of the 'ice-cream' that is bounded by x2 + y2 + z2 = 77 and the upper cone z2 = 3x2…

A: We have to find the volume of the 'ice -cream' that is bounded by the sphere  x2+y2+z2 = 77 and the…

Q: R is the region bounded by x2 + y – 4 = 0 and x – y +2 = 0 and it is revolved about y = 0.

A:

Q: evaluate the arca of He reginn bounded below by and y= aboue by y=X

A:

Q: Evaluate this integral Sc v – 2x)dy – (yx – x²)dx where C is a curve consisting of C, which is a…

A:

Q: I Sketch the area bounded by x² + 2y = 4 and x+y+2=0 and determine: d) area using horizontal strip…

A:

Q: Find bounded by y Ax+l and y=lx vying area doble ntorgral. -l. 2

A:

Q: Compute 6xy da dy, where D is bounded by the curves y = 4 – x2 and y = 2x + 4.

A:

Q: хе? -dA 4-y b- Ris bounded by x=0,x=2,y=0,^y=4-x?

A: Find the double integration of the given function:

Q: The area bounded by the curve y = In(z) and the lines z = 1 and =2 above the z -azis is %3D square…

A:

Q: he area bounded by y = |x| and the lines x = 1 and x = 1.7 is

A:

Q: 23) Find the area of plate bounded by y = x- 1, y = 3-x and y = 0.

A:

Q: Find the area of the reyion R boundedby and the liney=x+2 *-y-y and the line y =-x

A: We have to find are between the curves.

Q: Compute for the area of the region bounded by x = 1, x = 2, y = (x – 1)? – 2, and y = (x – 3)² + 2.…

A: From the given curves the bounded region is as shown below: Now use the double integral method to…

Q: Let f(x, y) = xcosy-y e*y. fry at (1,0)is equal to:

A:

Q: Evaluate the line integralf, (xy + z)ds along the line segment C from (1,2,3) to (-1,1,5).

A:

Q: Compute the area bounded by y = 12 – x, y=Vx and y = 1. Show all necessary workings.

A: Here , y=12-x , y=x and y=1 We need to compute the area bounded by these curves. Area is given by…

Q: How would I go about solving ∭xzdV, where E is bounded by the planes z = 0, z=y, and the cylinder x2…

A: We will find out the limits first.

Q: Find the area bounded between two curve by using Simpson' 3/8rule y=Vx+2 x=2 y = x+1

A:

Q: R is the region bounded by y = x², y = 4x - x² and the line x = and it is revolved about y = 0.

A: Given regions are, y=x2y=4x-x2y=0 Now, using Washer method by the formula, V=π∫abR2-r2dx

Q: Find the area bounded by x = y + 2, x = 1 - y^2, and the lines y = 1 and y = −1. *

A:

Q: . SS, xcos(y)dA, D is bounded by y = 0,y = x² ,x = 1.

A: See the details solution in below

Q: 4 SET UP AN INTEGIUL fonila fen SUifACE Arfer BounDED By Y=x-2y, x-C , Y=3, Auo x 20 CHEN ReTATowh…

A: The integral for finding surface area of the solid obtained when the region rotated about y axis is…

Q: Iculate the integral (2² - y2) dA nain D is bounded by y = r and y = 4x for I > 0. ving of the…

A:

Q: Find the area of shaded region by using Trapezoidal rule YA 2.5 x = y 1.5- 1- y = In 2 0.5- x= e?y…

A:

Q: what is the area of space bound between y=x^2 and y=x^3?

A:

Q: 2)Evaluate er dA , Ris bounded by y = x2,y 1 3)Evaluate I| Vy2 + 1dA , Ris bounded by x = 4 - y? ,x…

A:

Q: Find the volume of the 'ice-cream' that is bounded by x² + y2 + z2 = 10 and the upper cone z2 = 4x2…

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.