Start with the area bounded by y=x^2 , y=0 and x=2, then rotate around the line y=4.

Q: How can you sometimes find the area bounded by a parametrized curve and one of the coordinate axes?

A: Let the equation of parametrized curve be

Q: Find the area bounded by the parabola y2 − 3x + 3 = 0 and the line x = 4. With illustrations please

A:

Q: By integration, determine the area bounded by the curves y = 6x – x ^2and y = x^2 – 2x.

A:

Q: The area between the two curves in the picture is

A: GIven functions are, y1=4y2=x2The given graphs are symmetric about y axis.The points of intersection…

Q: Find the equation of the vertical line that divides the area of the region R bounded by 1 y = 20x2…

A: Identify the limits of integration from the given region, to calculate the area of the region. Here,…

Q: Find the area between the curves.

A: First sketch the region bounded by the curves x=1,  x=6,  y=1x  and  y=12 as shown below.

Q: Find the area between the two curves on [2,3]. y = ex y = (1/x)

A:

Q: Find the area bounded by the curve: y = 8x – x² and y = 3x

A: a) Consider

Q: Find the line y=mx that divides the area under the curve y=x(1-x) over [0,1] into two regions of…

A: Given,           The line y = mx that divides the area under the curve y = x(1-x) over [0,1] into…

Q: Find the area bounded by the curve y^2 = 4x and the line 2x + y = 4.

A: Given curves are  y2=4x, 2x+y=4 The region bounded by the above curves  is the yellow colored region…

Q: Find the area between the curves. x = -2, x = 1, y = 2x, y = x2 - 3

A: Given curves,  y = 2x y = x2 - 3 x = -2 x = 1 To find the area enclosed.

Q: 4 y = 1 + x4' y = 2x2

A:

Q: What is the area between y = 0, y = 3x2, x=0, x = 2?

A:

Q: Find the area bounded by the curve y=x^2 − 4, the lines y = 0 and x = 4

A: The graph is shown below:

Q: Find the line y = mx that divides the area under the curve y = x(1 − x) over [0, 1] into two regions…

A:

Q: Find the area bounded by the curve 2x2 + 4x + y – 0 and the line y + x = 0

A: To find the area of region bounded by the given curves.

Q: Find the area of the region bounded by the curve y = 9 - x2 and the x-axis.

A:

Q: If we want to find the area between the curves x = −y 2 + 1 and x = y 2 − 1, shall we integrate with…

A: Given curves are x=-y2+1 and x=y2-1

Q: Find the area bounded by the curve y²=9x and its latus rectum

A: Given equation is y2=9x the equation of parabola is of the form  y2=4axlatus rectum x=a  and…

Q: The curves x = 4y - y^2 and x = 2y - 3. Set up a single integral that evaluates the shaded area and…

A: Given  x=4y-y2 ,x=2y-3  To find  Area between  given curve using single integration method

Q: Find the area bounded by y = 3x² - 3 and y = 3. Leave your answer %3D correct to 2 decimal places.

A: Given  y = 3x2  -3  and y = 3 To find : Area bounded.

Q: Find the area bounded by x2- 6x +y = 0, x² - 2x - y = 0. and the x-axis.

A: We have given two curves;

Q: Determine the area of the triangle bounded by the coordinate axes and the tangent to x² - y = 0 at x…

A:

Q: Find the area of the surface formed by revolving the graph y=x on the interval [0,3] about x-axis.

A:

Q: What is the area bounded by the curves x = 1/y, 2x - y = 0, x = 6, and the x-axis?

A:

Q: 2 y : 1+x² ve y = x² %3D

A:

Q: Find the area bounded by the curve y = 9 – x2 and the x-axis.

A: Area

Q: Write expressions for the area enclosed by a curve interms of line integrals around .

A: Green's theorem transforms the line integral around C into a double integral over the region inside…

Q: Determine the area bounded by the curve y = 2x - x^2 + 5 and the line joining the points (3,2) and…

A: Please see the explanation below

Q: Two curves having an equation of 2y² and y = 2x² x = intersect each other. Compute the area between…

A: A detailed solution is given below.

Q: Find the area of the region bounded on the left by the curves y = e3x and y=3-x, and on the right by…

A: The area is the amount of space occupied by the surface. It is measured in terms of unit squares it…

Q: Calculate the area between the curves y = 7- 2x2, y = x2 + 4, and the x-axis.

A:

Q: estimate the area under the curve y=x^1/2, from x=1 to x=3 using right end point estimate

A: SolutionGiventhe curve y=x,from x=1tox=3 we need to estimate the area  under the curve y=x1/2,from…

Q: Find the moment of inertia with respect to x-axis of the area bounded by the parabola y = 4x and the…

A:

Q: Find the area bounded by the curve y=x3. -x2+3x and the line y=x. 16 4

A:

Q: Find the area bounded by the curve ay²=x³ and the line x=4a. With sketch please.

A: Area problem....

Q: The area bounded by the curve y = 6x and the lines x = 7,x = 11 and x – axis ахis is

A: → y = mx is the equation of straight line passing through origin with slope m.→ Area of triangle =…

Q: Calculate the area between the curves x = 1– y² by the line x = y² – 1.

A:

Q: find the area between the two curvesx=2-y^2x=y^4

A: Given thatx = 2-y2         ...(1)x = y4            ...(2)

Q: Find the volume generated by revolving about the line x=0 the area under the arch of the sine curvey…

A:

Q: Compute the area bounded by the curve y=3x² and the lines y=0 and x = 3,

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find the area bounded by the curve x = y^2 + 2y and the line x = 3

A:

Q: By integration, determine the area bounded by the curves y = 6x – x2 and y = x2 – 2x.

A:

Q: Find the area bounded by the curve 4y² + 16x – 15 = 0 and the linex = -1. %3D

A:

Q: Determine the area bounded by the curves x^3 - y = 0 and y + 3x^2 - 4 = 0, using a vertical element.…

A:

Q: find area between line y=-2+x and y=x^(1/2) and x-axis

A:

Q: Find the area bounded by the curves y - x² = -3,x+y = 3 and y = 0.5x.

A:

Q: Find the area of the region bounded by the line y = 2x – 5 and the parabola y = x² – 4x. - -

A: Graph of enclosed region -

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.