Find the area bounded by the ff. curves and lines: a. the loop of y^2 = x^4 (5 - x) b. x^2 - y^2= 9 and y= 2x - 6 c. an arch of y =(1/3)sin(x/3) d. y = xe^– x , the x-axis and the maximum ordinate.

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

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Q: Find the area bounded by tHe curves y=8x-x and y= 3x

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Q: Find the area of the region bounded by the parabola y=5x^2, the tangent line to the parabola is at…

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Q: Determine the area bounded by the curves y=sinhx, y=coshx, the y-axis and the line y=1.

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

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Q: Find the area of the region bounded by the curves y= 2² - 3 and y = 2x + 5.

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

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

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Q: Find the area of the region bounded by the curve y = x^3 + 3x and the lines x = −2, x = 2 and the…

A: Topic = Application of integration

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

A: a) Consider

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

A: The area is bounded by the given curves x3-y=0 and y+3x2-4=0. The main objective is to determine the…

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 AREA BOUNDED BY THE PARABOLA x = 8+2y-y², THE Y-AXIS, AND THE LINES y = -) AND y = 3

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

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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: 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: The area bounded by the parabola y = 4x2, y-axis and the lines y = 1, y = 4 is

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

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

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Q: Find the area between the curves. y = x5 - 2 ln (x + 5), y = x3 - 2 ln (x + 5)

A: Given: y=x5-2lnx+5y=x3-2lnx+5

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

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Q: Find the area of teh region bounded by y=5x/x2+2, x=1, x=5, y=0. Sketch the graph

A: We graph the region using a graphing calculator.

Q: find the area of the region bounded by the curves 4x - y2 = 0 and y = 2x - 4

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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: Find the area between the curves. x = -2, x = 1, y = 2x2 + 5, y = 0

A: Given, x=-2,x=1,y=2x2+5,y=0

Q: What is the area bounded by the curve y^2 = x and the line x - 4 = 0?

A: We have to determine area of bounded

Q: Find the area of the region in the first quadrant bounded by the line y = 8x, the line x = 1, the…

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

A: Area problem....

Q: Find the enclosed area by the curve with equation y=x^2-9 and x-axis in the region[-1,2]

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

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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 b0 und by Curves the y3= X-3

A: The region is bounded by y=9x2-36, y=0, x=1 and x=3

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

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

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

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Q: Find the area of the region in the first quadrant bounded by the line y=3​x, the line x=4​, the…

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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 between the curve y = √2x — 1 and the lines x = 1 and x = 5.

A: Given: The region between curve y=2x-1 and lines x=1 and x=5

Q: What is the area bounded by the curve y^2=x and the line x-4=0?

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

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

A: Given : Curve : y²= 4x              and line  2x+y=4 To find : Area between the curve and line

Q: Sketch the region bounded by the line y -axis. = 2 and the graph of y = sec2 x for −π2 < x <…

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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.