Find the area between y = x^2 + 4, x = 1 and y = 0.

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

A: See below

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

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

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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: 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 curve f(x) = (2+x)(x – 5), the lines = -2, line = 0 and the x - axis.

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Q: Find the area between the curves. x = -3, x = 0, y = 1 -x2, y = 0

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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: Calculate the area of the segment cut from the curve y = x(3 – x) by the line y = x.

A: here we have to find the area of the region bounded by the curve and line.

Q: Find the area between the curves. x = 0, x = 6, y = 5x, y = 3x + 10

A: Given: The curves x=0, x=6, y=5x, and y=3x+10 . The bounded area between the given curves is shown…

Q: The graphs of y = 1 − x2 and y = x4 − 2x2 + 1 intersect at three points. However, the area between…

A: Given curves  y=1-x2 y=x4-2 x2+1 Graph :

Q: Find the area between the curve y = 4 – x² and the line y = -x + 2.

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

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Q: Find the area of the region bounded by y = 10x + 4, y = -10x + 3 and x = 14. Leave your answer…

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

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

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

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Q: Find the area bounded by the curve y = 3x – x3 and the line y = 2

A: Given: y= 3x-x3; y=2 If f(x)> g(x) in the interval x=a to x=b, then the area between two curves…

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 of the region bounded by y = 5x², y=0, x= 4, x = 6. Give your answer to the nearest…

A: Sol:- The area between curves is the area between a curve fx and a curve gx on an interval a, b…

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

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Q: Find the area bounded by y2  = 4x and 2x - y = 4.

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Q: Find the area between the curves. x = -5, x=2, y = 3x, y = x² - 4

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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: Solve the area bounded by the curve y=x^2+2 and the line y=-x, x=1 and x=-2. With graph

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Q: solve the area bounded by the curve y=4x-x^2 and the lines x=-2 and y=4

A: To find out the area bounded by the curves.

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 area between the curve y = 9 − (x/2)^2 and the line y = 6 − x.

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Q: Find the area bounded by y=2*, y = 2x2, the y - axis and x = 1 Write your final answer in two…

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

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

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

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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: What is the area (in square units) of the region bounded by the graphs of y=x+2, and the x axis from…

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Q: Find the area bounded by y=2%, y = 2x2, the y - axis and x = 1 Write your final answer in two…

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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: y=9-x2 and ミ-4

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Q: Use double integration to find the area bounded by the given curves

A: Note: since you posted multiple question, as per our guidelines we are supposed to solve one…

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

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

A: integration gives the area of any function y .

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

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

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

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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.