Find the area bounded by the curve 5y^2 = 16x and the curve y = 8x – 24.

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 curve y = x exp(-x²), the x-axis and the vertical line passing through…

A: Given: The given curve is, The x-axis and the vertical line passing through the maximum coordinate.…

Q: Find the area bounded by the curve y=4x-x² and the lines x=-2 and y=4.

A: See below

Q: Estimate the area between the curve y = x^2 - 2x + 5 and the x-axis between x = 0 and x = 3 using 6…

A: Given, y=x2-2x+5 Here, a=0, b=3 and n=6 Therefore, ∆x=b-an3-06=12=0.5 Therefore the intervals are,…

Q: Find the area bounded by the curve y2 = 4x and the line 2x + y = 4.

A: so we have and the other function is

Q: Find the area bounded by the indicated curves. y = x4 - 18x? + 81, y = 81 - x

A:

Q: Determine the area bounded by the curves y = -x² – 18x + 63 and y = (x – 3)². |

A:

Q: Find the area bounded by the curve y = 4x over the square root of (1 - 2x) and lines y = 0, x = -4…

A:

Q: Estimate the area under the curve y=64-x^3 between x=0 and x=4. Use four rectangles

A:

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 bounded by the curves y2= 6x and x2 = 6y?

A: topic - area bounded by curves

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: Determine the area bounded by the curves y = -x² – 16x + 36 and y = (x – 2)².

A: Answer

Q: Find the area of the propeller-shaped region enclosed by the curve x - y3 = 0 and the line x - y =…

A: x-y3=0  &  x-y=0⇒y3=x  &  y=x⇒y=x13  &  y=x Now the diagrammatic representation of the…

Q: Determine the area bounded by the curves x³ - y = 0 and y + 3x² - 4 = 0, using a vertical element.

A:

Q: Find the area bounded by the curve y = x² – 3x 3x and y + 4 = 0

A: We have to compute the area of the region bounded by the curve y=13x3-3x and the line y=-4 using the…

Q: Find the area under the curve y = 3xe for æ > 3. area =

A: Given:The given curve is y=3xe-x and x≥3To find:we have to find the area under the curve

Q: Find the area bounded by the curve y = 4x - x² and and the lines x = 0 and y = 4. %3D Answer:

A: we can find the area between the curve and the lines by integrating the curve function through lines…

Q: Find the area bounded by the curves y= 5x and y = 15x.

A:

Q: Find the area bounded by the curve y = 2x + x² – x³, the x-axis and lines x = 0 and x = 1. %3D

A:

Q: How can you determine the you must use vertical strip instead of horizontal strip in getting the…

A: We can also compute areas by slicing horizontally instead of vertically.  In this case, we'll denote…

Q: Find the area bounded by the curve x=y²+2y and the line x=8.

A:

Q: y = 4 – x2 y = 4 – 4x - -5-

A: Definition used -             The area between two curves f(x) and g(x) -…

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

A:

Q: Find the area above the curve y=lnx in the lower half-plane between x=0 and x=1.

A:

Q: Find the area on the first quadrant bounded by the curve y = 2Vx and the lines y = 1,x = 4 and the…

A:

Q: Find the area of the region between the curves 4x + y = 12 and x = y. Area between curves

A: Solution

Q: Find the area of the region bounded by the curve  y = 2x2 - x  and the line  y = x + 4  .

A: To find the area of the curve.

Q: $ find the area of region in the first quadrant bounded on the left by the y-axis, below by curve x…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Find the area between the curves: y=x^3−10x^2+21xx and y=−x^3+10x^2−21x

A:

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 area bounded by the curve y=9-x^2 and the x-axis

A:

Q: Find The Area Enclosed by the Curve x=7²-2t,y-VE and the Y-pris

A:

Q: Find the area between the curves y = 4x – 3 and y = x². %3D

A: Given data is : y=4x-3     .....1 y=x2      .....2 From equation (1) and (2) ,…

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 of the region between the curves 4x + y = 12 and x = y. Area between curves =

A: R

Q: Determine the area bounded by the curves Y = -x² – 18x + 88 and y = (x – 4)².

A: To determine the area bounded by the curves

Q: Find the area of the region bounded by the curve y= 1--x² and the x-axis.

A: Given equation of the curve: y=1-19x2 To find: Area of the region bounded by the curve and x-axis.

Q: Find the the Yegion bounded by area y= tanx 4

A: integration gives the area of any function y .

Q: Find the area between the curves. 3x 3x x-0, x-D4, y3D2e" y-e

A:

Q: Find the area bounded by the curves, 2x² + 4x + y =0 and y = 2x.

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 -

Q: Find the area of the region bounded by the curve y=1--x2 and the x-axis. 9

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.