1. Find the area of the region bounded by y^2=8x and y=x

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

A: See below

Q: y = ln x and x - y -4 = 0

A: Explanation of the answer is as follows

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

A:

Q: 8. Find the area bounded by x² – 6x + y = 0, - x² – 2x – y = 0, and the x – axis.

A:

Q: Sketch the region bounded by the graphs of the functions. y = x2 – 8x + 16, y = x2 – 24x + 144, y =…

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Q: 4. Find the area of the region in the first quadrant bounded on the left by the y-axis, below by the…

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Q: Find the area of the region bounded by the graphs of the equations. y = 4x + 2, x = 0, x = 2, y = 0

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Q: . Find the area bounded between the curves 5x-y x2 and y = 3x + x²

A: We have the given the curves y=5x-x2 and y=3x+x2 We have to find the area bounded by this two given…

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

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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: What is the area bounded by the curve x² = -9y and the line y + 1 = 0?

A: Given curve is x2=-9y Line is y+1=0 We need to find the area bounded by the curve

Q: What is the area of the region between the graps y = x – 1 and line y = -x – 1

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

A: Answer

Q: Determine the area of the region bounded by x=--y2  +10 and x=(y -2)2

A:

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

A: 2. The area bounded by the curve y=4-x2 and the x-axis Note:    Multiple questions are given, we are…

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 exact area of the region bounded by y = -x² + 3x +1 and y = -x+1

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Q: The bounded by y= xx*+1, area of the region axis. y=x, x-- 3, and

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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: 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: ded by the curve or line: y2+4x-8=0, Y

A: Given that: The equation of the curve y2 + 4x - 8 = 0. The equation of the line y = 2x.

Q: Find the area of the region bounded by the given curves. y = 9x2 ln(x),  y = 36 ln(x)

A: First of all, consider the given equations and assume them as f (x) and g (x). Equate f (x) = g (x)…

Q: Sketch the region bounded by the graph of y= (½)x² + 1 and thex-axis between x =--2 and x= 4. Set up…

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Q: Calculate the area bounded by x (x-4) + y = 0 and the lines x + 2 = 0; y - 4 = 0.

A: We can evaluate the unshaped surfaces by using triple or double integral technique.

Q: Find the area between the curve x = y2 and the line x = y + 2 Solution : * with respect to x:

A: Given curves x=y2. . . . 1x=y+2. . . . .2 Equating (1) and (2) y2=y+2y2-y-2=0y-2y+1=0y=2,-1

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

A:

Q: Find the area between y=ln(x-6) and y = (ln(x-6))2

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Q: What is the area of the region between the graphs of y=x^2 and y=-x from x=0 to x=2?

A: The equation of the curves are : C1 : y = x2C2 : y =-xC3 : x = 0C4 : x = 2 To evaluate : The area of…

Q: Compute the area bounded by the curves x=2y² and x=4+y²

A: Area bounded by two curves x=f(y) and x=g(y) is given by, A=∫abf(y)-g(y)dy ,a,b are the points of…

Q: 1. Find the area of the region bounded from the right by the curve x = 4 - y2 , from the left by the…

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Q: Find the area under the curve y = lines x = 1 and x = 5. 3x² + 4x + 1 bounded by the x-axis and the

A: Area under the curve y=3x2+4x+1 bounded by x-axis and x=1 to x=5.

Q: Find the area of the region enclosed between the curves y= 4 -x^2 and x=3 and x-axis within the…

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Q: area bounded between y=3x+2 and y=-x^2+2

A: here we have to find the area bounded between the curve y=3x+2......(1) and y=-x2+2x+4.....(2)

Q: Find the area between the curves.    x = - 5, x = 1, y = 10 x, y= x 2 -11

A:

Q: 2. Find the area of the region bounded by the graphs of y = x2 – 6 and y – 3 = 0. - -

A: Graphically: Now, the area can be found as the following.…

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

A:

Q: What is the slope of the curve y = ex at x = ln 2? What is the area of the region bounded bythe…

A: Consider the curves, y=ex,x=ln2 Differentiating with respect to “x” then, dydx=ddxex=exTo  calculate…

Q: Calculate the area under the curve y between x = 2 and x 8. %3D

A: Since you have posted multiple questions therefore we will answer the first one for you. If you want…

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: 10. Find the area bounded by 2. Hhe curves y=8x-x²0ind y=3x

A: topic - area bounded by curves

Q: What is the area of the region between the graphs of y = x3 and y = -x from x = 0 to x = 2

A: Area between curves

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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Q: find the area of the region bounded by the curve y=x2 - 4x+3  , x axis and the lines x=2 and x=4

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

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Q: Sketch the region bounded by the graphs of the functions and find the area of the region y = x³ – 4x…

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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.