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

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 parabola y^2=4x and the line 2x-4. (with graph)

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 area between the curves. y = x2 - 18, y = x - 6

A: y = x2 - 18, y = x - 6

Q: What is the area of the region between the lines y = 7x and y = 3x from x = 1 to x = 4?

A: 1.

Q: Find the area between the curve y=4x-x² and the x-axis

A:

Q: Find the area bounded by the curve y = 62xe-62x and the x axis from x =0 to x = 4

A: Area bounded by the curve y=f(x) and x-axis from x=a to b is given as, ∫abf(x)dx Some common…

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: Solve the area bounded by the curve y=5-x^2 and the line y=2x. With graph.

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 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. 3x х%3 -2, х%34, у%33е3X, у%3D2е 3X +1

A:

Q: Find the area enclosed between the curve y = 9 - x squared and line y = x + 7

A: This question is based on application of integration.

Q: Find the area bounded by the curve y2 = 4x and the line 2x + y = 4 and provide a correct and…

A:

Q: Find the area between the curves: y = x³ – 10x? + 16x - x³ + 10x² – 16x 3 and y = -x° + 10x?

A: Consider the figure given below :

Q: Find the area between the two curves y = x^2 and y = 2x – x^2

A: Given:     To determine: The area between the two curves.

Q: Please estimate the area under the curve c(x)=1−x3 for 0≤x≤1 using 4 rectangles with width 1/4.

A:

Q: Find the area between the curves. x = -2, x = 4, y = 3e3x, y = 2e3x + 1

A: The above question is from the application of the integration part and since the major part of…

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 curves y= 5x and y = 15x.

A:

Q: By double integration, Find the area between the line y=6-2x, the x-axis and y-axis.

A:

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

A: Area

Q: FInd the area bounded by the give curves y=6x2-8x-2 and y= 3x2+4x-11

A:

Q: Find the area between the curves -4x + y = 16 and -2x2 = -y+ 10.

A:

Q: Find the area between the curves. y = x4/3, y = 2x1/3

A: y = x4/3, y = 2x1/3

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

A:

Q: Find the area between the curves x = 10 − y2 and y = x − 8

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 enclosed by the curves x = -2, x = 3, y = 3x2 - 70, and y = 12x + 26.

A: Consider the area enclosed by the curves x = -2, x = 3, y = 3x2 - 70, and y = 12x + 26.

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

A:

Q: Find the area between the curves x2 and 6x – 5

A:

Q: Find the area between the curves y = 4x° and y= 3x + 1.

A: Given the curves y=4x2 and curve y=3x+1. We need to find the area between two curves.

Q: Find the area between the curve and the x-axis over the indicated interval. y = 25 - x2; [-5, 5|

A:

Q: Find the area between the curves x=y^2/2 and y=x-4

A: First we draw the curves using graphing calculator.

Q: y=9-x2 and ミ-4

A:

Q: Find the area between the curves. y=x² - 23, y = 9 – 4x

A:

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

A:

Q: Estimate using right-hand endpoints, the area between the curves y=9x^2 +30 and y= 5-7x over the…

A: given :

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 of the region between the curves 4x + y = 12 and x = y. |3D Area between curves =

A:

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

A:

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

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.