.X = -3 Q3. The region bounded by the curve y = x2 and the line y = 3x, is revolved about the line x = -3. Find %3D its volume generated. 4 3 :y = x2 -2 -1 0 2 3 y = 3x

Q: Find the area of the region bounded by the parabola y² = 2x - 2 and the line y = x - 5. 16 17 18 19…

A:

Q: 14 12

A:

Q: 3. Find the z= 4 a. area bounded by the curve ay² = z* and the line Ans. 141 a².

A:

Q: Find the area of the shaded region. y (1, 7e) 15 y = 7 e 10 5 y=7xe -1.0 -0.5 0.5 1.0 1.5 2.0 20

A:

Q: Find the area of the region bounded by the parabola y² = 2x2 and the line y = x - 5. 16 17 18 19…

A: Given: y2=2x-2 and y=x-5 Now find the point of intersection between the given curves. y2=2x-2 ;…

Q: 1. Find the area of the region enclosed by the equations below. y = x² – 2x and y = x

A: Given function :

Q: 6. Consider the region bounded by the function y = 4x, and the lines x = 0 and x = 3. Then the area…

A:

Q: 2. Find the area of the region enclosed by the parabola y = 2x² and the line y = -x-1

A:

Q: Determine the area of the region between the following curve. x = |y| and 2x = −y^2 + 2

A: Given that, x = |y| and 2x = −y2 + 2

Q: Find the area between the y-axis and the graph X = Y 7 6 5 4 X 543-2/1² 1 2 3 4 5 WŃ y - 1 on the…

A: Here we have to use the concept of integration

Q: Find the area of the shaded region. (-5е — 5) 2 y 14 (1, 5e) 12 10 y = 5 e 8 6. 2 y = 5xe -1.0 -0.5…

A: The area of the given shaded region which is bounded by the curve y=5ex , y=5xex2  and x=0  is…

Q: Consider the following equations. x = y2 + 5, x = y + 7 Sketch the region bounded by the graphs of…

A: To find the area of the region for the curve x=y2+5 and the line x=y+7

Q: Find the area of the region bounded by the parabola y² = 2x − 2 and the line y = x − 5. 16 17 18 19…

A: y² = 2x -2  y = x -5  Here we have to find intersection point  x = (y² +2)/2  x = y+5  Compare both…

Q: Find the number k > 1 such that the region bounded by the curves y = 1, y = x-2, and x = k k has…

A: Given curves are y=1 and y=x-2 and interval is x=1 to x=k

Q: In the given question  find b such that the line y b divides the region bounded by the graphs of the…

A: Given :           Equation of curves as :                  y = 9 - x , y = 0 Formula :           A =…

Q: || 2. Find the area of the region enclosed by the curves x = 2y² – y + 1 and x y² + y + 4.

A: The area between two curves is given by: Where a and b are intersection points of the curves f and…

Q: 3) Find the area of the region enclosed by the following line and the curve. y = x – 1 and y² = 4x +…

A: The graph for the given functions y=x-1 and y2=4x+1 is shown below.

Q: Find the area of the region(s) enclosed by the curve y= |2x-6|, the x-axis, and the lines x =0 and x…

A:

Q: f(x)=x^2+5x+10, y=0, x=-4, x=8 Approximate the area between the given curves using 4 rectangles of…

A: The interval of interest is x∈[-4,8]. Hence, dividing this interval into 4 equal intervals will give…

Q: Find the area of the region bounded by the curves y = y = -x² + 4x. 9/4 11/3 12/15 8/3 none of the…

A:

Q: o. Find the area of the region bounded by the curve y =x csc²x, the x axis 1 and the lines x = 1 =t…

A: Answer and explanation is given below

Q: Find the area of the shaded region. y 14 (1, 5e) 12 10 y= 5 e 8 2 y= 5 xe -1.0 -0.5 0.5 1.0 1.5 2.0

A: Given,  The graph of  y = 5ex  and  y=5xex2  Point of intersection of the graph is 1, 5e  We have to…

Q: The area bounded by the curve y = 3/T and the lines e = 5 and a = 9 above the a – axis is square…

A: First of all find all meeting points then calculate the area.

Q: y = x³ + 2x? – 8x, y = x³ + 5x? -

A:

Q: Given the curve y = x´ and the lines y = 0 and y = 2 – x Find the area of the region bounded by the…

A: Given

Q: Find the area of the shaded region. У 14 (1, 5e) 12 10- y = 5 e* y = 5x e х -0.5 0.5 1.0 1.5 2.0…

A: The area of the shaded region can be calculated using  integration. The following integral is set up…

Q: (10,00 Puanlar) 6- Find the area of the region bounded by the curves y - 3x = 4 and 3x- 2y = 11. 134…

A: The given curves are: y2-3x=43x-2y=11

Q: 1/ Find the area of the region enclosed between the curves y= 2x²+10 and y=4x+16 and ,x=-2 and x-5?…

A:

Q: 30. Find the area bounded by the curve 5y²=16x and the curve y²=8x-24. A. 36 B. 25 C. 16 D. 14

A: Topic = Area

Q: 2 Find the area of the region bounded by the curve y2 =4x and the lines x = 1 and x = 4. A. 24…

A: Given y2=4x X=1 and x=4

Q: 1.1. The area of the region bounded by the curves y = V, y=1 and a 4 is equal to A. 3 square units…

A: NOTE: Refresh your page if you can't see any equations. . to find the intersecting point, compare…

Q: f(x)=7x^2+20, y=0, x=-3, x=8 Approximate the area between the given curves using 4 rectangles of…

A:

Q: 2. Find the area of the region enclosed by æ + y? = 0 and ¤+3y² = 2.

A:

Q: 5 m 4m 4 m 3 m 3 m Find the area of the region bounded by the graphs of y2 = 4x and the line 2x - y…

A:

Q: 1 2. Find the total area of the region between the curve and the x-axis. a. y=2-x; b. y= 3x-3;…

A:

Q: 3. Find the area of the region enclosed by the two curves y = x² and y = -2x² + 3x.

A:

Q: The area of the region enclosed by y = 49(x + 1)ez, y = 49e7z, x = 1 and x = 12 is

A: Solution is given below :

Q: 3) Find the area of the region bounded by the lines y = 0, 2x = 3y, 3x = -4y + 10, and y + 3 = (x -…

A:

Q: the region described. 5 1 ded by y = 7 and y = 4 2 1-X egion is approximately

A:

Q: 2. Find the area of the region enclosed by the curves and x, 0 < *< 2. y = y = (x2 + 1)2 4*

A:

Q: 2. Find the area bounded by the line x – 2y + 10 = 0, the x- axis, the y – axis and x 10.

A: The red line is x=10 and the blue line is given line i.e. x-2y+10-0 Given x-2y+10=0This can be…

Q: Areas of regions Find the area of the following regions.

A: Given that, y=10x2-2x-24

Q: R is the region bounded by x = y? + 1 and x = 9 – y² and the axis of revolution is x = 9.

A: Given that,

Q: 5. I Find the area of the region enclosed by the curves y = 3x³ - x²-10x and y=2x-x². (x ≥ 0) (a)…

A:

Q: Find the exact area of the region bounded by 2y = 4√√x, y = 4, and 2y + 2x = 6

A: Here we have to find the area of the region.

Q: The area bounded by the curve y = 3/x and the lines x 3 and x = 8 above the x axis is _square units…

A: All options are incorrect.

Q: Find the area of the region enclosed by the curve y=e¬5x and the lines y=1 and x=2. .e-10 + 으 10 10…

A:

Q: 5. Consider the region bounded by the function y = 4x, and the lines x = 0 and x = 3 Then the area…

A: We know  that the area under the graph of a continuous function f (x) between the vertical lines x =…

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.